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Math Help - integration help!

  1. #1
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    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.

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  2. #2
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    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?

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  3. #3
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    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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  4. #4
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    Quote Originally Posted by DarthPipsqueak View Post
    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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