# Integral solving problem

lukatwo

## Homework Statement

I've been trying to integrate the following: ∫[STRIKE]$\frac{cos^3(x)}{\sqrt{sin(x)}}$[/STRIKE]dx

## The Attempt at a Solution

First, I substituted sin(x) with t, and got dt=cos(x)dx => dx=$\frac{dt}{cos(x)}$.
After that I got ∫[STRIKE]$\frac{cos^2(x)}{\sqrt{t}}$[/STRIKE]dt
Then i transformed cos^2(x) into 1-sin^2(x), and finally got to ∫[STRIKE]$\frac{1-t^2}{\sqrt{t}}$[/STRIKE]dt

I thought I could just disintegrate them into two smaller integrals like ∫[STRIKE]$\frac{1}{\sqrt{t}}$[/STRIKE]dt - ∫[STRIKE]$\frac{t^2}{\sqrt{t}}$[/STRIKE]dt , and solve them easily, and then reverse the substitution.

Wolfram proposes that i cannot(?) do that, or rather prefers that I do another substitution.

I even tried to make it a defined integral, and calculate the values between the Wolfram solution, and my own. They differ by 0.1 or something similar.

Can someone explain what is the right way to do it?