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April 5th, 2014, 03:43 PM   #1
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I am stuck on an integral problem.

I apologize for the sloppy writing. I don't understand where the first two in the final row of my solution comes from. I know how to solve the rest. I just need to know where the "2-" comes from. Thank you.

P.S The final row should have the integral sign in the front.

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April 5th, 2014, 03:52 PM   #2
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Math Focus: Calculus/ODEs
Through your substitution, you have obtained:

$\displaystyle \int\frac{2u}{u+1}\,du$

Now, suppose we add zero to the numerator of the integrand as follows:

$\displaystyle \int\frac{2(u+1-1)}{u+1}\,du$

And then write it as:

$\displaystyle \int\frac{2(u+1)-2}{u+1}\,du=\int 2-\frac{2}{u+1}\,du$
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