Integration by Parts - Bruce E. Shapiro
Integration by Parts - Bruce E. Shapiro
Integration by Parts - Bruce E. Shapiro
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Math 150A TOPIC 6. INTEGRATION BY PARTS<br />
Exercises.<br />
Use integration <strong>by</strong> parts to solve the following integrals.<br />
∫<br />
6.1. tan −1 x dx<br />
∫<br />
6.2. x tan −1 x dx<br />
∫<br />
6.3. sin −1 (3x) dx<br />
∫<br />
6.4. t 2 e t dt<br />
6.5.<br />
6.6.<br />
6.7.<br />
6.8.<br />
6.9.<br />
6.10.<br />
6.11.<br />
∫ ln x<br />
√ x<br />
dx<br />
∫<br />
∫<br />
∫<br />
∫<br />
∫<br />
∫<br />
e x cos x dx<br />
x2 x dx<br />
x ln(2x) dx<br />
x 2 ln(5x) dx<br />
x 3 (x 2 + 7) 3/2 dx<br />
x 5<br />
√<br />
x3 + 5 dx<br />
Make a substitution then use integration <strong>by</strong> parts to solve the following<br />
integrals.<br />
∫<br />
6.12. (ln(3x)) 2 dx)<br />
∫<br />
6.13. ln √ x dx<br />
∫<br />
6.14. cos ln x dx<br />
∫<br />
6.15. e x sin −1 e x dx<br />
Page 20 « 2012. Last revised: February 26, 2013
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