# Thread: integration help!

1. ## integration help!

How do I integrate these problems?

integral[3/(x^2)(sqrt(25-x^2))]

aaaand if possible this one:

integral[(x^2)/sqrt(25-16x^2)

thank you so much! My book doesn't have any examples like this and I'm having trouble because I keep messing up somewhere in the problem.

2. Hello, DarthPipsqueak!

I hope you're familiar with Trig Substitution.
I'll get you started on the second one . . .

$\int \frac{x^2\,dx}{\sqrt{25-16x^2}}$

$\text{Let: }\:4x \:=\:5\sin\theta \quad\Rightarrow\quad x \:=\:\tfrac{5}{4}\sin\theta \quad\Rightarrow\quad dx \:=\:\tfrac{5}{4}\cos\theta\,d\theta$

$\text{And: }\;\sqrt{25-(4x)^2} \;=\;\sqrt{25- 25\sin^2\!\theta} \;=\;\sqrt{25(1-\sin^2\!\theta)} \;=\;\sqrt{25\cos^2\!\theta} \;=\;5\cos\theta$

$\text{Substitute: }\;\int\frac{\overbrace{\left(\tfrac{25}{16}\sin^2 \!\theta\right)}^{x^2} \overbrace{\left(\tfrac{5}{4}\cos\theta\, d\theta\right)}^{dx}}{\underbrace{5\cos\theta}_{\s qrt{25-16x^2}}} \;=\;\frac{25}{64}\int \sin^2\!\theta\,d\theta$

Can you finish it now?

3. Thank you so so so much! Yes, i can definitely take it from here. I think i was just having trouble getting to that point. I appreciate your help!!!

4. Originally Posted by DarthPipsqueak
Thank you so so so much! Yes, i can definitely take it from here. I think i was just having trouble getting to that point. I appreciate your help!!!
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