Soal Latihan Integral Dasar

1. d(4x+1) = 4dx

2. d(3-3x) = -3dx

3. d(5t+2) = 5dt

4. d(10-t) = -1dt

5. d(7-4u) = -4du

6. d(9u+2) = 9u

7. d(2s+4) = 2ds

8. d(1-8s) = -8ds

9. d(4v-1) = 4dv

11. d(9) = 0dx

12. d(x3-2) = 3x2-2dx

13. d (2−x)3

Misal: u = (2-x) u’ = -1

v = u3v’ = 3u2

d (2−x)3=3u2u '

= 3¿

= 3(2−x )2

= (−6+3x )2 dx

16. d(2x+1) (3-x2)

Missal :u=2 x+1u ’=2

v = 3-x2 v’ = -2x

jadi d(2x+1) (3-x2) = u’v+uv’

= 2(3-x2¿+ (2 x+1 )−2

= 6-2x2+ (−4 x2−2x )

= -6x2-2x+6 dx

17. d(3x+2¿7

u = (3x+2) u’ = 3

y = u7 y’ = 7u6u '

y’ = 7(3x+2¿6(3)

f’ (x) = 7(3) (3x+2¿6

= 21 (3x+2¿6dx

18. d(6-5x¿3

Misal : u = 6-5x u’ = -5

y = u3 y’ = 3x2u’

y’ = 3(6-5x¿2-5

= -15 (6-5x¿2

19. d(2 x+1 )(6−7 x )

Misal : u = 2x+1 u’ = 2

v = 6-7x v’ = -7

jadi : d(2x+1)(6−7 x)

=u' v−uv 'v2

= 2 (6−7 x )−(2 x+1 )−7¿¿

= 12−14 x+14 x+736−84 x+49 x2

= 19

49 x2−84 x+36