Question

Integrate http://i.imgur.com/MbZTdPk.png

Answer 1

Attempt:
\[\LARGE \int\limits_{\frac{1}{3}}^1\frac{x^3(\frac{1}{x^2}-1)^\frac{1}{3}}{x^4}\]

Answer 2

now let \[\Large \frac{1}{x^2}=t\]

Answer 3

@INeedHelpPlease?
Only \[x^{-3}\]
will be outside the fraction term.

Answer 4

yeah sorry error in bracket

Answer 5

now

Answer 6

\[\LARGE \int\limits (t-1)^\frac{1}{3}\]
but what about limits?

Answer 7

In your substitution (2nd post); find t when x = 1/3
Similarly, find t when x = 1

That will be your limits in t

Answer 8

Some people prefer solving the indefinite integral first then substituting back to the original variable and finally putting the original limits.

Apparently, former is a quicker method.