TABLA DE INTEGRALES INMEDIATAS Funciones Simples Funciones compuestas Z Z Z Z Z Z Z Z Z Z Z xn+1 +C x dx = n+1 n n 6= −1 Z 1 dx = ln(x) + C x f 0(x).f (x)n dx = 1 f (x)n+1 + C n+1 f 0(x) dx = ln(f (x)) + C f (x) Z f 0(x)ef (x) dx = ef (x) + C Z f 0(x)af (x) dx = sen x dx = − cos x + C Z f 0(x) sen(f (x)) dx = − cos(f (x)) + C cos x dx = sen x + C Z f 0(x) cos(f (x)) dx = sen(f (x)) + C x x e dx = e + C 1 x a dx = a +C ln a x 1 dx = cos2 x Z (a > 0) 2 (1 + tg x) dx = tg x + C 1 − dx = cotg x + C sen2 x √ 1 dx = arc sen x + C 1 − x2 1 dx = arc tg x + C 1 + x2 Z Z Z Z n 6= −1 1 f (x) +C a ln a f 0(x) dx = cos2 (f (x)) − Z (a > 0) f 0 (x) 1 + tg2 (f (x)) dx = tg(f (x)) + C f 0 (x) dx = cotg(f (x)) + C sen2 (f (x)) p f 0 (x) 1 − (f (x))2 dx = arc sen(f (x)) + C f 0 (x) dx = arc tg(f (x)) + C 1 + (f (x))2