Question

∫[(x^4-9)^(-1/3)[4x^3],]dx=

Answer 1

let \[u=x^4-9\]

Answer 2

then
\[du=4x^3 dx\]

Answer 3

then
\[du=4x^3 dx\]

Answer 4

\[\int u^{-1/3} du\]

Answer 5

\[=\frac{3}{2} u^{2/3} +C\]

Answer 6

substitute back in to get in terms of x

Answer 7

\[\frac{3}{2} (x^4-9)^{2/3} +C\]

Answer 8

compute the derivative to check the answer