Calculus Final

Find the Indefinite Integral: S x sqrt(2x +1) dx

(1/10)(2x+1)^(5/2) - (1/6)(2x+1)^(3/2) +C

Evaluate the integral: S (t^2 +7t +9)dt

(t^3)/3 + (7t^2)/2 +9t +C

Integration by Parts: S x ln x dx

(x^2)/4 (2ln x -1)+C

Evaluate the integral: S8,-8 -6 ^3sqrtx^2 dx

-1152 / 5

Find the Indefinite Integral: S x^3 sqrt(x+2) dx

sqrt (x+2) [(2x^4)/9 +(4x^3)/63 - (16x^2)/105 + (128x)/315 - 512/315 ] +C

Find the derivative of the function: y= 11y^4 +5y^3 +5y^2 +11

y'= 44y^3 + 15y^2 +10y

Find the derivative of the function: y= 12z^4 - 4z +14

y'= 48z^3 - 4

Find the Indicated partial derivative: z= ln(x^3 y) ; zxx

zxx= - 3 / x^2

Use substitution to integrate the given funtion: S 6x/sqrt(5-5x^2) dx

- (6 sqrt (1-x^2))/sqrt 5 +C

Integrate using partial fraction decomposition: S (x-2)/[x(3x^2 + 7x +4)] dx

- (ln(x))/2 + 3ln(x+1) - 5/2 ln(3x +4) +C

Integrate using partial fraction decomposition: S (2x+1)/[x(2x^2 +x-6)] dx

- (ln(x))/6 -3/14 ln(x+2)+ 8/21 ln(2x-3) +C

Integrate using partial fraction decomposition: S (2-x)/[x^2 (x+4)] dx

-(3ln(x))/8 + 3/8 ln(x+4) - 1/2x +C

Use substitution to integrate the given funtion: S x/sqrt(9-2x) dx

-1/3 sqrt(9-2x) (x+9) +C

Use substitution to integrate the given funtion: S (2x-1)/(-6x^2 +6x+6) dx

-1/6 ln(x^2 -x-1) +C

Evaluate the integral: S32,0 -5 ^5sqrt(x^4) dx

-12800 / 9

Evaluate the integral: S2,1 -9x^3 dx

-135 / 4

Evaluate the integral: S243,-243 -7 ^5sqrt(x^4) dx

-153090

Evaluate the integral: S8,-8 -5 ^3sqrtx^2 dx

-192

Integrate using partial fraction decomposition: S [2(x+1)]/[x^2 (3x+2)] dx

-2(-(ln(x))/4 +1/4 ln(3x+2) -1/2x) +C

Integrate using partial fraction decomposition: S- 2/[x(x^2 +2x -6)] dx

-2(1/10 ln(x-2) -(ln(x))/6 +1/15 ln(x+3))+C

Integrate using partial fraction decomposition: S [2(x+1)]/ (6x^3 -7x^2 +1) dx

-2(1/2 ln(x-1) - 3/5 ln(2x - 1) + 1/10 ln(3x +4)) +C

Integrate using partial fraction decomposition: S - 2/[x(x^2 +2x -3)] dx

-2(1/4 ln(x-1) -(ln(x))/3 +1/12 ln(x+3))+C

Use substitution to integrate the given funtion: S sqrt(6-5x) xdx

-2/125 (6-5x)^3/2 (5x+4)+C

Use substitution to integrate the given funtion: S x/sqrt (8-3x) dx

-2/27 sqrt(8-3x) (3x+16)+C

Use substitution to integrate the given funtion: S x/sqrt(7-x) dx

-2/3 sqrt(7-x) (x+14) +C

Find the double Integral: S4,9 S16,1 sqrt x dxdy

-210

Evaluate the integral: S5,1 -9x^5 dx

-23436

Integrate using partial fraction decomposition: S (-x-1)/[x(2x^2 -9x +9)] dx

-4/9 ln(x-3) - (ln(x))/9 +5/9 ln(2x - 3) +C

Evaluate the integral: S5,-2 -4x^2 dx

-532 / 3

Find the double Integral: S2,-1 S0,-2 xdxdy

-6

Evaluate the integral: S4,1 -3/x^4 dx

-63 / 64

Evaluate the integral: S5,-1 -3x^5 dx

-7812

Use substitution to integrate the given funtion: S (70x -7)/(-5x^2 +x-4) dx

-7ln(5x^2 -x+4)+C

Evaluate the integral: S5,1 -2/(x^2) dx

-8 / 5

Use substitution to integrate the given funtion: S (24x -20)/sqrt(-3x^2 +5x +1) dx

-8 sqrt(-3x^2 +5x+1) +C

Use substitution to integrate the given funtion: S (48x +16) sqrt(-6x^2 -4x +7) dx

-8/3 (-6x^2 -4x+7)^3/2 +C

Evaluate the integral: S3,-1 -4x^3 dx

-80

Evaluate the integral: S2,-1 3/(x^2) dx

-9 / 2

Evaluate the integral: S243,0 -9 ^5sqrt(x^4) dx

-98415

Integrate using partial fraction decomposition: S (2-x)/(x+1)^2 dx

-ln(x+1) -3/(x+1) +C

Partial fractions Integration: S 3/(x^2 -3x) dx

-ln|x| +ln|x-3| +C

Find the double Integral: S1,-1 S1,-1 ydxdy

0

Find the double Integral: S2,-2 S3,-1 ydxdy

0

Find the double Integral: S2,0 S2,-2 xdxdy

0

Use substitution to integrate the given funtion: S x/(sqrt(4x+5)) dx

1/12 (2x-5) sqrt(4x+5) +C

Use substitution to integrate the given funtion: S x/(5x +3) dx

1/25 (5x+3) - 3/25 ln(5x+3)+C

Use substitution to integrate the given funtion: S 4x/(6x^2 -6) dx

1/3 ln(x^2 -1) +C

Use substitution to integrate the given funtion: S x/sqrt(-8x -5) dx

1/48 sqrt(-8x -5) (5-4x) +C

Use substitution to integrate the given funtion: S (30x +5)/sqrt(3x^2 +x-3) dx

10 sqrt(3x^2 +x-3) +C

Use substitution to integrate the given funtion: S (10x +25)/sqrt(x^2 +5x -8) dx

10 sqrt(x^2 +5x-8) +C

Find the double Integral: S16,0 S36,9 sqrt x dydx

1152

Find the double integral: S5,1 S-2,-3 xdydx

12

Find the double Integral: S4,0 S4,1 sqrt y dxdy

16

Find the double Integral: S1,0 S4,0 sqrt y dydx

16 / 3

Evaluate the integral: S1,0 4 ^4sqrtx^3 dx

16 / 7

Find the double Integral: S9,0 S9,0 sqrt y dxdy

162

Find the double Integral: S2,0 S2,1 9dydx

18

Evaluate the integral: S4,-2 8x^2 dx

192

Integrate using partial fraction decomposition: S - [2(x-1)]/[x(2x-30] dx

2((ln(x))/3 +1/6 ln(2x-3)) +C

Integrate using partial fraction decomposition: S [2(x-1)]/[x(3x^2 +8x+4)] dx

2(- (ln(x))/4 - 3/8 ln(x+2) +5/8 ln (3x+2)) +C

Integrate using partial fraction decomposition: S 2/[x(6x^2 +5x -6)] dx

2(- (ln(x))/6 + 2/39 ln(2x + 3) + 3/26 ln(3x-2)) +C

Integrate using partial fraction decomposition: S 2/[x(x^2 -x-6)] dx

2(-1/15 ln(x-3) +(ln(x)/6 - 1/10 ln(x+2)) +C

Integrate using partial fraction decomposition: S [2(x-1)]/[x(2x^2 -7x+3)] dx

2(2/15 ln(x-3)+(ln(x))/3 +1/5 ln(2x-1)) +C

Integrate using partial fraction decomposition: S [2(x-1)]/[x(x+2)] dx

2(3/2 ln(x+2) - (ln(x))/2) +C

Use substitution to integrate the given funtion: S sqrt(2-6x) xdx

2/135 sqrt(2-6x) (3x-1)(9x+2)+C

Use substitution to integrate the given funtion: S x/sqrt(-7x-8) dx

2/147 sqrt(-7x-8) (16-7x) +C

Use substitution to integrate the given funtion: S x/sqrt(3x-5) dx

2/27 sqrt(3x-5) (3x+10)+C

Integrate using partial fraction decomposition: S (x-1)/(x-3)x dx

2/3 ln(x-3)+(ln(x))/3 +C

Use substitution to integrate the given funtion: S x sqrt(9x +9) dx

2/5 (x+1)^3/2 (3x-2) +C

Use substitution to integrate the given funtion: S x/sqrt(-5x -1) dx

2/75 sqrt(-5x-1) (2-5x)+C

Integrate using partial fraction decomposition: S - [2(x+1)]/x^2 dx

2/x -2ln(x) +C

Find the double Integral: S-2,-3 S0,-1 x^2 + y^2 dydx

20 / 3

Evaluate the integral: S2,-1 -7x dx

21 / 2

Evaluate the integral: S5,-1 5x62 dx

210

Find the double Integral: S9,0 S16,4 sqrt y dxdy

216

Find the double Integral: S9,4 S9,1 sqrt 4 dydx

260 / 3

find the double integral: S0,-3 S3,0 ydydx

27 / 2

Find the double Integral: S0,-1 S3,1 x^2 +y^2 dxdy

28 / 3

Find the double Integral: S1,0 S-1,-3 x^2 + y^2 dxdy

28 / 3

Integrate using partial fraction decomposition: S (2-x)/[x(x+1)^2] dx

2ln(x) - 2ln(x+1) + 3/(x+1) +C

Integrate using partial fraction decomposition: S (2-x)/ [x(x+1)] dx

2ln(x) - 3ln(x+1) +C

Integrate using partial fraction decomposition: S (-x-2)/(x-1)x dx

2ln(x) - 3ln(x-1) +C

Integrate using partial fraction decomposition: S (x-2)/(x-1)x dx

2ln(x) - ln(x-1) +C

Find the double Integral: S0,-3 S0,-1 e^x dxdy

3- (3 / e)

Partial fractions Integration: S 3/(x^2 -9) dx

3/2 ln|x-3| + 3/2 ln|x+3| +C

Find the double Integral: S3,1 S2,-1 x62 +y^2 dydx

32

S243,0 3 ^5sqrt(x^4) dx

32805

Find the double Integral: S36,0 S36,9 sqrt y dxdy

3888

Partial fractions Integration: S 3x/(x62 -6x +9) dx

3ln|x-3| - 3/(x-3) +C

Find the double Integral: S-1,-2 S3,-1 xdxdy

4

Find the double Integral: S0,-1 S2, -1 x^2 +y^2 dxdy

4

Find the double Integral: S1,0 S4,0 xydydx

4

Evaluate the integral: S3,-3 -2/x^2 dx

4 / 3

Find the double Integral: S1,-2 S3,-1 e^x dydx

4(-(1/e^2)+e)

Integrate using partial fraction decomposition: S (x+1)/[(x-3)x] dx

4/3 ln(x-3) - (ln(x))/3 +C

Find the double Integral: S1,-1 S3,-1 6dxdy

48

Find the double Integral: S4,0 S5,1 ydydx

48

Find the double Intergral: S2,-2 S3,0 4dxdy

48

Find the double Integral: S4,1 S2,-1 xy dxdy

48 / 4

Use substitution to integrate the given funtion: S (10x-15)/(x^2 -3x -7) dx

5ln(x^2 -3x-7) +C

Evaluate the integral: S5,1 6/x^3 dx

72 / 25

Use Lagrange Multipliers to find the indicated Extrema: Maximize f(x,y,z)=xyz subject to x + y + z - 6=0

8

Use Lagrange Multipliers to find the indicated Extrema: Minimize f(x,y) = x^2 + y^2 subject to x + y=4

8

Find the double integral: S2,-2 S1,-3 e^x dydx

8 sinh(2)

Find the double Integral: S2,-1 S4,1 xdydx

9 / 2

Find the double Integral: S4,1 S4,1 10dydx

90

Find the double Integral: S25,1 S16,4 sqrt y dxdy

992

Use substitution to integrate the given funtion: S (144x +27)/(8x^2 +3x +1) dx

9ln(8x^2 +3x +1)+C

Find a and b so that f(x) = ax + b has a minimum sum of squared errors for the points (-3,0), (-1,1), (1,1),(3,2)

a = 3 / 10 and b = 1

Find a and b so that f(x) = ax + b has a minimum sum of squared errors for the points (2,4), (3,5), (4,7)

a = 3 / 2 and b = 5 / 6

Integration by Parts: S xe^x dx

e^x (x-1) +C

Find the derivative of the function: f(x) = 4e^-2x

f'(x) = - 8e^-2x

Find the derivative of the function: f(x) = -8e^2x

f'(x) = -16e^2x

Find the derivative of the function: f(x) = 7e^(2x^2)

f'(x) = -28xe^(-2x^2)

Find the derivative of the function: f(x) = 8e^(-4x^2)

f'(x) = -64xe^(-4x^2)

Find the derivative of the function: f(x) = -6e^-2x

f'(x) = 12e^-2x

Find the derivative of the function: f(x) = 9e^-3x

f'(x) = 27e^-3x

Find the Indefinite Integral: S x^2 / (x+1)^3 dx

ln |x+1| + 2/(x+1) - 1/2(x+1)^2 +C

Integration by Parts: S lnx dx

x ln(x) - x+C

Find the Extrema using the first partials test: f(x,y)= xy - (1/4)x^4 - (1/4)y^4

x= 1,0,1 and y=1,0,1

Find the derivative of the function: y= sqrt(13x^2 +10x)

y' = (13x +5)/sqrt(13x^2 +10x)

Find the derivative of the function: y= ^3sqrt(15z62 +15)

y' = (2 ^3sqrt5 z)/[3^(2/3) (z^2 +1)^(2/3)]

Find the derivative of the function: y= ^5sqrt y (10y^2 +5)

y' = (22y^2 +1)/y^(4/5)

Find the derivative of the function: y = ln{ (2x-1)/x^3}

y' = (3-4x)/(x-2x^2)

Find the derivative of the function: y= ^4sqrty (6y +11)

y' = (30y + 11)/4y^(3/4)

Find the derivative of the function: y= ^4sqrt x (5x^2 +3x +7)

y' = (45x^2 +15x +7)/ 4x^(3/4)

Find the derivative of the function: y= (9-7z)/(8z+5)

y' = - 107/(8z +5)^2

Find the derivative of the function: y= (5-4x)/(8x-4)

y' = - 3/(2(2x - 1)^2)

Find the derivative of the function: y= ln{ [(7x-1)^5] / 256x^4 }

y' = -(7x+4)/(x-7x^2)

Find the derivative of the function: y= -3z

y' = -3

Find the derivative of the function: y= (5z +5)/(6z -6)

y' = -5/[3(z-1)^2]

Find the derivative of the function: y= (3z +4) / (9z -7)

y' = -57/(9z - 7)^2

Find the derivative of the function: y = ln{ 1/(7x -2)^2}

y' = 14/2-7x

Find the derivative of the function: y= ln{ (2x-2)^5 /(5x-2)^2

y' = 15x / (5x^2 -7x + 2)

Find the derivative of the function: y= ^5sqrtz (x+9)

y' = 3(2z +3)/5z^(4/5)

Find the derivative of the function: y= ^5sqrtz (x+9)

y' = 3(2z+3)/5z^(4/5)

Find the derivative of the function: y= ^4sqrt x (6x +6)

y' = 3(5x +1)/2x^(3/4)

Find the derivative of the function: y=^4sqrtx (6x +6)

y' = 3(5x+1)/2x^(3/4)

Find the derivative of the function: y= sqrt(10x +14)

y' = 5/(sqrt2 sqrt(5x+7))

Find the derivative of the function: y= (5y-8)/(7y+4)

y' = 76/(7y +4)^2

Find the derivative of the function: y= ln{ (8x+2)^3 / (4x+2)}

y' = [2(8x+5)] / (8x^2 +6x +1)

Find the derivative of the function: y= 10/x

y'= - 10/x^2

Find the derivative of the function: y= -9 ^5sqrt y

y'= - 9/5y^(4/5)

Find the derivative of the function: y= 3/x^5

y'= -15/x^6

Find the derivative of the function: y= -6z^4 +4z^3 -8z^2 +5z -8

y'= -24z^3 + 12z^2 - 16z + 5

Find the derivative of the function: y= -2z^2

y'= -4z

Find the derivative of the function: y= 6/z

y'= -6/z^2

Find the derivative of the function: y= (5z+4) / (8z-9)

y'= -77 / (8z-9)^2

Find the derivative of the function: y= -5z^2

y'= 10z

Find the derivative of the function: y= ^5sqrt(3z^2 +16z +2)

y'= 2(3z+8)/5(3z62 +16z +2)^(4/5)

Find the derivative of the function: y= -9/z^3

y'= 27/z^4

Find the derivative of the function: y= (8-6x)/(2x-9)

y'= 38/(2x-9)^2

Find the derivative of the function: y= -19z^4 + 4z + 12

y'= 4-76z^3

Find the derivative of the function: y=8sqrt y

y'= 4/sqrt y

Find the derivative of the function: y= 10x^4 -x^3 -7x

y'= 40x^3 -3x^2 -7

Find the derivative of the function: y= 10y^4 -11y^2 -3y-15

y'= 40y^3 -22y-3

Find the derivative of the function: y= 14y^4 +7y^3 +9y -9

y'= 56y^3 +21y^2 +9

Find the derivative of the function: y= -12z^3 -2z^2 -7z +9

y'=-36z^2 -4z -7

Find the derivative of the function: y= -8/x^3

y'=24/x^4

Find the derivative of the function: y=3y

y'=3

Find the derivative of the function: y=2z^3

y'=6z^2

Find the Indicated partial derivative: z= -5e^(y^3) x ; zx

zx= -5e^(y^3)

Find the Indicated partial derivative: z=ln(xy^2) ; zx

zx= 1 / x

Find the Indicated partial derivative: z= ln(x^2 y^4) ; zx

zx= 2 / x

Find the Indicated partial derivative: z=ln(x^2 y^2); zx

zx= 2 / x

Find the Indicated partial derivative: z=x^2 - 12yx +4y^2 ; zx

zx= 2x -12y

Find the Indicated partial derivative: ln((x^3)y^3) ; zx

zx= 3 / x

Find the Indicated partial derivative: z= -x^2 +yx +2y^2 ; zx

zx=y-2x

Find the Indicated partial derivative: z= -12e^(x^4) y ;zxx

zxx= -192e^(x^4) yx^6 -144e^(x^4) yx^2

Find the Indicated partial derivative: z= -12x^2 +11yx -2y^2 ; zxx

zxx= -24

Find the Indicated partial derivative: z= -4x^2 y^4 - xy^3 ; zxx

zxx= -8y^4

Find the Indicated partial derivative: z= 11e^(y^4) x ; zxx

zxx= 0

Find the Indicated partial derivative: z=6x^2 +10yx -5y^2 ; zxy

zxy= 10

Find the Indicated partial derivative: z=11(x^4)(y^4) + 3(x^2)y ; zxy

zxy= 176(x^3)(y^3) +6x

Find the Indicated partial derivative: z=xy^2 -11xy^4 ; zxy

zxy= 2y - 44y^3

Find the Indicated partial derivative: z=11e^(x^2) y^2 ; zxy

zxy= 44e^(x^2) xy

Find the Indicated partial derivative: z=-2e^(y^2)x^2 ; zxy

zxy=-8e^(y^2)xy

Find the Indicated partial derivative: z=ln(x^3 y); zxy

zxy=0

Find the Indicated partial derivative: z=-7(y^3)(x^4) -3(y^4)(x^3) ; zy

zy= -21(y^2)(x^4) -12(y^3)(x^3)

Find the Indicated partial derivative: -7e^(y^4) x^2 ; zy

zy=28e^(y^4) x^2 y^3

Find the Indicated partial derivative: z=10e^(y^3) x ; zy

zy=30e^(y^3) xy^2

Find the Indicated partial derivative: z=(x^4)(y^4) ; zy

zy=4((x^4)(y^3))

Find the Indicated partial derivative: z=-8x^2 +yx-3y^2 ; zy

zy=x-6y

Find the Indicated partial derivative: z=ln(x^3 y^4); zyy

zyy= - 4 / y^2

Find the Indicated partial derivative: z= -10e^(x^4) y^2 ; zyy

zyy=-20e^(x^4)

Find the Indicated partial derivative: z=4e^(x^4) y ; zyy

zyy=0