Question

Evaluate the integral 1/[x^(2/3)*(9+x^(1/3))]
How to solve it?

Answer 1

Try \(u=9+x^{1/3}\)

Answer 2

\[
du=\frac 13 x^{-2/3}dx
\]

Answer 3

\[
\int \frac 1{9+x^{1/3}}(x^{-2/3}dx)\to\int \frac 1u\;(3du)
\]

Answer 4

ah ok i got it now, thank you so much ^_________^

Answer 5

Prodigious!