Calc antiderv integrations

Constant Multiple Rule

∫ kf(u) du = k∫ f(u) du

Sum/Difference Rule

∫[f(u) ± g(u)] du = ∫f(u) du ± ∫g(u) du

Integral of 1

∫ du = u + C

Power Rule

∫u^n du = u^(n+1)/(n+1) + C, n ≠ -1

Integral of 1/u

∫(1/u) du = ln|u| + C

Integral of e^u

∫e^u du = e^u + C

Integral of a^u

∫a^u du = a^u/ln(a) + C

Integral of sin(u)

∫sin(u) du = -cos(u) + C

Integral of cos(u)

∫cos(u) du = sin(u) + C

Integral of tan(u)

∫tan(u) du = -ln|cos(u)| + C

Integral of cot(u)

∫cot(u) du = ln|sin(u)| + C

Integral of sec(u)

∫sec(u) du = ln|sec(u) + tan(u)| + C

Integral of csc(u)

∫csc(u) du = -ln|csc(u) + cot(u)| + C

Integral of sec(u)tan(u)

∫sec(u)tan(u) du = sec(u) + C

Integral of csc(u)cot(u)

∫csc(u)cot(u) du = -csc(u) + C

Inverse Sine Form

∫ du/√(a²-u²) = arcsin(u/a) + C

Inverse Tangent Form

∫ du/(a²+u²) = (1/a)arctan(u/a) + C

Inverse Secant Form

∫ du/[u√(u²-a²)] = (1/a)arcsec(|u|/a) + C