List of integrals (PDF format)

Integrals of simple functions1 Rational functions(∗)(∗)∫∫dx = x + Cx n dx = xn+1n + 1 + Cif n ≠ −1(∗)(∗)2 Logarithms∫∫ 1xdx = ln |x| + Cdua 2 + u 2 = 1 a arctan u a + C∫ln x dx = x ln x − x + C∫log b x dx = x log b x − x log b e + C3 Exponential functions(∗)∫∫e x dx = e x + Ca x dx = axln a + C

4 Irrational functions(∗)∫∫∫du√a2 − u 2 = arcsin u a + C−du√a2 − u 2 = arccos u a + Cduu √ = 1 |u|arcsecu 2 − a 2 a a + C5 Trigonometric functions(∗)(∗)∫∫∫∫∫∫∫∫∫∫∫∫∫sin x dx = − cos x + Ccos x dx = sin x + Ctan x dx = − ln |cos x| + Ccot x dx = ln |sin x| + Csec x dx = ln |sec x + tan x| + Ccsc x dx = − ln |csc x + cot x| + Csec 2 x dx = tan x + Ccsc 2 x dx = − cot x + Csin 2 x dx = 1 (x − sin x cos x) + C2cos 2 x dx = 1 (x + sin x cos x) + C2sin n x dx = − sinn−1 x cos xncos n x dx = − cosn−1 x sin xn+ n − 1n+ n − 1narctan x dx = x arctan x + ln √ 1 + x 2 + C∫∫sin n−2 x dxcos n−2 x dxNote. The most important integrals are indicated with (∗)