Need help with integration question: integral of (4X^2)/(X^2+9)

[calchelpneeded]

I know that this problem was posted previously, but I didn't really understand the answer that was provided.
The problem says to evaluate the integral of: (4X^2)/(X^2+9).
I don't know how to approach this problem.
Thank you for your help!

 

[Deleted member 4993]

I know that this problem was posted previously, but I didn't really understand the answer that was provided.
The problem says to evaluate the integral of: (4X^2)/(X^2+9).
I don't know how to approach this problem.
Thank you for your help!

Have you been taught trigonometric substitution?

 

[calchelpneeded]

Have been taught trigonometric substitution?

I might have been in calc 1, but it has been 2 years since then so I really don't remember haha

 

[calchelpneeded]

I may have been in calc 1 but that was 2 years ago so I really don't remember how to do it.

 

[Deleted member 4993]

I know that this problem was posted previously, but I didn't really understand the answer that was provided.
The problem says to evaluate the integral of: (4X^2)/(X^2+9).
I don't know how to approach this problem.
Thank you for your help!

To understand the solution - you'll need to review your calc (specially trig substitution)

\(\displaystyle \displaystyle{\int \dfrac{4x^2 dx}{x^2 + 9}}\)

\(\displaystyle =\displaystyle{4 * \int \left [1 - \dfrac{9 }{x^2 + 9}\right ]dx}\)

Now substitute

x = 3 * tan(Θ) → dx = ?

continue.......