Antiderivative Rules

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∫xⁿdx

((xⁿ⁺¹)/(n+1))+c

∫du/(u*√u²-a²)

(1/a)(sec⁻¹(|u/a|)+c

∫du/a²+u²

(1/a)(tan⁻¹(u/a))+c

∫a^xdx

(a^x)/(lna)+c

∫sin(x)dx

-cos(x)+c

∫csc²(x)dx

-cot(x)+c

∫csc(x)cot(x)dx

-csc(x)+c

∫tan(x)dx

-ln|cos(x)|+c

∫f(g(x))g'(x)dx

F(g(x))+c

∫e^xdx

e^x+c

∫kf(x)dx

k*F(x)+c

∫kdx

kx+c

∫(g'(x)/g(x))dx

ln|g(x)|+c

∫sec(x)dx

ln|secθ+tanθ|+c

∫cot(x)dx

ln|sin(x)|+c

∫(1/x)dx=∫fx⁻¹dx

ln|x|+c

∫secxtanxdx

sec(x)+c

∫(1/(x√x²-1))dx

sec⁻¹(|x|)+c

∫cos(x)dx

sin(x)+c

∫du/√a²-u²

sin⁻¹(u/a)+c

∫(1/(√1-x²))dx

sin⁻¹(x)+c

∫sec²(x)dx

tan(x)+c

∫(1/(1+x²))dx

tan⁻¹(x)+c

∫[f(x)±g(x)]dx

∫f(x)dx±∫g(x)dx


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