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Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent.

$\int \frac{d x}{e^{x}\left(3 e^{x}+2\right)}$

$-\frac{1}{2 e^{x}}+\frac{3}{4} \ln \left|\frac{2+3 e^{x}}{e^{x}}\right|+C$

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All right. So for this question, we could be right this as e to the power off Negative X divided by three e to the power off X plus two times D s. So few plants into a computer algebra system Or your calculator supports this kind of these kind of questions You end up with three times ln of three e to the power of explosive to minus two e to the power of negative X minus three acts divided by four by four plus C. And this is the exact answer, as he would get if you use your table of integral tze and did this question manually.

University of California, Berkeley