Question

Integral subtitusi

∫ x^3 / ( x^4 -1)^20 dx =

Answer 1

∫ x^3 / ( x^4 -1)^20 dx =
misal:
u = x^4 - 1
du = 4x³ dx
1/4du = x³ dx

∫ x^3 / ( x^4 -1)^20 dx = ∫1/u^20 1/4 du
=1/4 ∫1/u^20 du
= 1/4 ∫u^-20 du
= 1/4 (1/-19 u^-19 + C)
= (-1/76 + C) / ((x^4 + 1)^19)