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JH

# (a) Use a computer algebra system to find the partial fraction decomposition of the function$$f(x) = \frac{4x^3 - 27x^2 + 5x - 32}{30x^5 - 13x^4 + 50x^3 - 286x^2 - 299x - 70}$$(b) Use part (a) to find $\int f(x) dx$ (by hand) and compare with the result of using the $CAS$ to integrate $f$ directly. Comment on any discrepancy.

## (a) $\frac{24,110 / 4879}{5 x+2}-\frac{668 / 323}{2 x+1}-\frac{9438 / 80,155}{3 x-7}+\frac{(22,098 x+48,935) / 260,015}{x^{2}+x+5}$(b) $\frac{4 \mathrm{s} 22}{4879} \ln |5 x+2|-\frac{34}{323} \ln |2 x+1|-\frac{3146}{80,155} \ln |3 x-7|+\frac{11,049}{200,015} \ln \left(x^{2}+x+5\right)$$\quad+\frac{75,772}{260,015 \sqrt{19}} \tan ^{-1}\left[\frac{1}{\sqrt{19}}(2 x+1)\right]+C$

#### Topics

Integration Techniques

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

JH

#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp