06.07 Integrating Using Substitution

Using the substitution u is equal to the square root of x plus 2 comma integral from 2 to 7 of x times the square root of the quantity x plus 2 end quantity times d times x is equal to which of the following?

2 times the integral from 2 to 3 of the quantity u to the fourth power minus 2 times u squared end quantity times d times u

Find integral of e to the power of x divided by the quantity 1 plus e to the power of 2 times x end quantity times d times x.

arctan e^x + C

Evaluate integral of cosine of the quantity 4 times theta minus 2 end quantity times d times theta.

one fourth sine of the quantity 4 times theta minus 2 end quantity plus C

Evaluate integral from pi over 2 to pi of negative cosine x sine x dx.

one half

Evaluate integral of square root of the quantity x plus 2 end quantity times d times x.

two thirds times the quantity x plus 2 end quantity to the three halves power plus C