04/19/23 Perkins

AP Calculus AB

Day 11Section 4.5

Integration by Substitution

'f g x g x dx F g x C

making f u d uF Cu where a d 'nu g x du g x dx

521. 1x x dx

'f dx Fx g x g x Cg

2 1u x

2du

xdx

2du xdx

512 u du 61

12 u C

62112 1x C

5212 1 2x xdx

2. 5cos 5x dx

42 33. 1x x dx

5u x

5du

dx

5du dx

cos 5 5x dx cos u du

sinu C

sin 5x C

3 1u x

23du

xdx

23du x dx

43 21x x dx 43 21

3 1 3x x dx 41

3 u du 51

15 u C 53115 1x C

24. sin 3 cos 3x x dx sin 3u x

3cos 3du

xdx

3cos 3du x dx

213 sin 3 3cos 3x x dx

213 u du

319 u C

319 sin 3x C

Perkins

AP Calculus AB

Day 11Section 4.5

Integration by Substitution

'f g x g x dx F g x C

521. 1x x dx

2. 5cos 5x dx

42 33. 1x x dx

24. sin 3 cos 3x x dx