Calc help pleaseeee?

Question

If you use substitution x=3sin(t) for the integral of 4x/(9-x^2)^(5/2) what integral results?

Answer 1

Step 1:

The integration is .

Consider .

Substitute and in the above integral.

                          

Step 2:

Now assume

Substitute and   in the above integral expression.

                        

Substitute in the above expression.

                        

We have , using Pythagorean theorem .

Substitute in the above expression.

                          

.

Solution :

.