| Find the antiderivative |
Find the antiderivative shown WITHOUT the use of a calculator or computer system that does algebra. Explain your method clearly.
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Problem Moderated by: MrT |
| Problem Solution |
The quickest way to compute this is to use long division to break the expression into two parts. When you divide this out, you get
4x + (3x^2+1)/(x^3+x).
The integral of the first term is simply 2x^2, while the second can easily be done by u-substitution, and recognizing that it is a natural log. The answer is:
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