Integrals — Formula Sheet

∫ f(x) dx = F(x) + C

∫_a^b f(x) dx = F(b) - F(a)

A(x) = ∫_a^x f(t) dt

A'(x) = f(x)

∫ x^n dx = x^(n+1)/(n+1) + C, n ≠ -1

∫ dx = x + C

∫ cos x dx = sin x + C

∫ sin x dx = -cos x + C

∫ 1/x dx = log|x| + C

∫[f(x)+g(x)]dx = ∫f(x)dx + ∫g(x)dx

∫k f(x)dx = k∫f(x)dx

∫f'(x)dx = f(x) + C

Substitution: x = g(t), dx = g'(t)dt

Partial fractions

Integration by parts: ∫f(x)g(x)dx = f(x)∫g(x)dx - ∫[f'(x)∫g(x)dx]dx

The power rule for integration excludes n = -1.