## anonymous 5 years ago ive been asked to find the integral using subtitution 6x^5/(5+x^6)^4dx

$\int\limits[(6x ^{5})/(5+x ^{6})^{4}]dx$ So if you set u = 5+x^6 then du = 6x^5 dx Now substituting back into the original gives us: ∫du/u^4 which is ∫u^(-4)du = (-1/5) u^(-5) + c The last step is to plug back in for u to get: (-1/5)(5+x^6)^(-5) + c or -1/[5(5+x^6)^5] + c