Megan M.

asked • 09/29/16# Calculus 2 Integration

^{x}to express the integrand as a rational function with three linear factors in the denominator, one of which is u, and then evaluate the integral.

^{x}-20)/(e

^{2x}+5e

^{x}+4)

## 2 Answers By Expert Tutors

Eric C. answered • 09/29/16

Engineer, Surfer Dude, Football Player, USC Alum, Math Aficionado

^{x}

^{2}= (e

^{x})

^{2}= e

^{2x}

^{2x}+ 5e

^{x}+ 4

^{2}+ 5u + 4

^{x}- 20

^{x}

^{x}+ 4) - 1/(e

^{x}+ 1)

^{x}+ 4) - 1/(e

^{x}+ 1) dx

^{x}from each denominator

^{x}(1 + 4/e

^{x}) - 1/e

^{x}(1 + 1/e

^{x}) dx

^{x}

^{x}dx

^{x}dx

^{x}

^{x}dx

^{x }dx

^{x}) + ln(1 + 1/e

^{x}) + C

^{-x}(e

^{x}+ 4)) + ln(e

^{-x}(1+e

^{x})) + C

^{x}+ 4) - x + ln(e

^{x}+ 1) + C

^{x}+ 4) + ln(e

^{x}+ 1) + C

Michael J. answered • 09/29/16

Mastery of Limits, Derivatives, and Integration Techniques

**(**-17e

^{x}- 20

**)**/

**(**(e

^{x})

^{2}+ 5e

^{x}+ 4

**)**dx

^{x}into the integral, we get

**[**(-17u - 20) / (u

^{2}+ 5u + 4)

**]**du

**[**(-17u - 20) / (u + 4)(u + 1)

**]**du

**[**(-17u - 20) / (u + 4)(u + 1)

**]**du = ∫

**[**A / (u + 4) + B / (u + 1)

**]**du ---> setup 1

**[**

**(**A(u + 1) + B(u + 4)

**)**/ (u + 4)(u + 1)

**]**du ---> setup 2

^{x}.

Megan M.

^{x}+4)-ln(e

^{x}+1) but webwork is telling me that this is incorrect. Do you see what I did incorrectly?

09/29/16

Eric C.

09/29/16

Megan M.

09/29/16

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