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Worksheet 7.2 - Integration by Parts · PDF file08.02.2013 · 7.! e √ x dx...

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Worksheet 7.2 - Integration by Parts February 8th, 2013 u dv = uv v du b a u dv = uv b a b a v du 1. x cos 2x dx 2. sin 1 x dx 1
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Page 1: Worksheet 7.2 - Integration by Parts · PDF file08.02.2013 · 7.! e √ x dx Hint: Make a t-substitution first, and then use integration by parts. 8.! sin(lnx) dx 4

Worksheet 7.2 - Integration by PartsFebruary 8th, 2013

!u dv = uv −

!v du

! b

a

u dv = uv""ba−! b

a

v du

1.

!x cos 2x dx

2.

!sin−1 x dx

1

Page 2: Worksheet 7.2 - Integration by Parts · PDF file08.02.2013 · 7.! e √ x dx Hint: Make a t-substitution first, and then use integration by parts. 8.! sin(lnx) dx 4

3.

!e3x cos 2x dx

4.

! 2

0

xe2x; dx

2

Page 3: Worksheet 7.2 - Integration by Parts · PDF file08.02.2013 · 7.! e √ x dx Hint: Make a t-substitution first, and then use integration by parts. 8.! sin(lnx) dx 4

5.

! e

1

x2 ln x dx

6.

!(ln x)2 ; dx

3

Page 4: Worksheet 7.2 - Integration by Parts · PDF file08.02.2013 · 7.! e √ x dx Hint: Make a t-substitution first, and then use integration by parts. 8.! sin(lnx) dx 4

7.

!e√x dx Hint: Make a t-substitution first, and then use integration by parts.

8.

!sin (lnx) dx

4


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