(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://www.wolframalpha.com/input/?i=integrate+%281%2F%28%28x^2%29sqrt%2825-%28x^2%29%29%29

3. The attempt at a solution

Alright, so I attempted this integral and checked my answer on wolfram and my answer was the same except for a -sin(^-1)(x/5) tagging along in mine. I can't figure out why that shouldn't be there.

Here's what I did:

1) Factored a 5 out of the root, so the problem then looked like:

(1/5)∫(1/((x^2)(sqrt(1-(x/5)^2)))

2) Set up trig substitutions:

sec(t)=sqrt(1-(x/5)^2)

x=5sin(t)

dx=5cos(t)

3) Do the substitution

(1/5)∫(5cos(t)/(25(sin(t)^2)sec(t)))dt

*cancel 5s, pull 25 out, replace sec(t) with 1/cos(t) yields:

(1/25)∫(cos(t)^2)/(sin(t)^2)dt

4) Replace cos(t)^2 with 1-sin(t)^2 and break up the fraction to get:

(1/25)∫((csc(t)^2)-1)dt

5) Integrate that, yielding:

(1/25)(-cot(t) - t)

Now, substituting the x's back in for t gives the answer on wolfram plus -(sin(x/5)^-1) which comes from solving for t using trig.

Did I screw something up to give me the -t at the end? I know I haven't done these in a while but I can't figure out where I went wrong.

Thanks!

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# Homework Help: Calc II Integral

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