1. Integration problem

$\displaystyle $\int tan^3(x) sec^4(x) dx$$

I first tried substituting $\displaystyle $u = tan(x)$$, then I tried substituting $\displaystyle $u = sec(x)$$, but I couldn't seem to solve it.

Any hints?

2. Originally Posted by BrownianMan
$\displaystyle $\int tan^3(x) sec^4(x) dx$$

I first tried substituting $\displaystyle $u = tan(x)$$, then I tried substituting $\displaystyle $u = sec(x)$$, but I couldn't seem to solve it.

Any hints?
$\displaystyle \int tan^3(x)sec^4(x)$ cab be written as

$\displaystyle \int tan^3(x)sec^2(x)sec^2(x)$

$\displaystyle \int tan^3(x)[1 + tan^2(x)]sec^2(x)$

Now simplify and solve.

3. $\displaystyle tan^2(x)+1=sec^2(x)$

4. Thank you!