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int( ((20*x)/((x^2)-25)), x ). My solution was 10x^2*ln(x^2-25). In the right solution, the x^2 outside the ln is not there, why?

 Mar 24, 2016
 #1
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Answer a different question first.

What do you get if you differentiate

\(\displaystyle \ln(x^{2}-25)\) ?

 Mar 24, 2016
 #2
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Factor out constants:
  =  20 integral x/(x^2-25) dx
For the integrand x/(x^2-25), substitute u = x^2-25 and  du = 2 x  dx:
  =  10 integral 1/u du
The integral of 1/u is log(u):
  =  10 log(u)+constant
Substitute back for u = x^2-25:
Answer: |  =  10 log(x^2-25)+constant   

 Mar 24, 2016

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