CK-12-Calculus

7.2. Integration By Parts http://www.ck12.org

; Math Video Tutorials by James Sousa, Integration by Parts (10:03)

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URL: http://www.ck12.org/flx/render/embeddedobject/597

; Math Video Tutorials by James Sousa, Integration by Parts, Additional Examples (7:48).

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URL: http://www.ck12.org/flx/render/embeddedobject/598

Review Questions

Evaluate the following integrals. (Remark:Integration by parts is not necessarily a requirement to solve the integrals.
In some, you may need to useu−substitution along with integration by parts.)

1.∫ 3 xexdx

2.∫x^2 e−xdx

3.∫ln( 3 x+ 2 )dx

4.∫sin−^1 xdx

5.∫sec^3 xdx

6.∫ 2 xln( 3 x)dx

7.∫(lnxx)^2 dx

8. Use both the method ofu−substitution and the method of integration by parts to integrate the integral below.
   Both methods will produce equivalent answers.

∫

x√ 5 x− 2 dx

9. Use the method of tabular integration by parts to solve∫x^2 e^5 xdx.


10. Evaluate the definite integral∫ 01 x^2 exdx.


11. Evaluate the definite integral∫ 13 ln(x+ 1 )dx.