04/19/23 Perkins

AP Calculus AB

Day 3Section 5.2

1du

uTheorem:

21. dx

x

ln u C

12.

4 1dx

x

12 dxx

2ln x C

4 1u x 4du dx

1 1

4du

u

1ln

4u C

1ln 4 1

4x C

2

43.

4 1

xdx

x

22

44.

4 1

xdx

x

2

4 8

8 4 1

xdx

x

24 1u x

8du xdx

1 1

2du

u

1ln

2u C

21ln 4 1

2x C

22

4 8

8 4 1

xdx

x

24 1u x 8du xdx

2

1 1

2du

u

21

2u du

11

2u C

1

2C

u

2

1

2 4 1C

x

4 2

2

35.

3

x x xdx

x

2 4 23 3x x x x

2x

4 23x x x

22 3

xx dx

x

22 3

xx

x

22 3

xx dx dx

x

3 21 1ln 3

3 2x x C

2 3u x 2du xdx

2 1

2

1x dx du

u

Simplify with long division.

Perkins

AP Calculus AB

Day 3Section 5.2

1du

uTheorem:

21. dx

x

12.

4 1dx

x

2

43.

4 1

xdx

x

22

44.

4 1

xdx

x

4 2

2

35.

3

x x xdx

x