Question

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

Answer 1

\[\int\limits[(6x ^{5})/(5+x ^{6})^{4}]dx\]
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