Integration Short Questions (Question 1)


Question 1:
Find the integral of each of the following. (a)  ( 3 x 2 5 2 x 3 +2 )dx (b)  x 2 ( x 5 +2x )dx (c)  3 x 4 +2x x 3 dx (d)  (7+x)(7x) x 4 dx (e)  (5x1) 3 dx (f)  3 ( 4x+7 ) 8 dx
Solution:
(a)
( 3 x 2 5 2 x 3 +2 )dx = ( 3 x 2 5 x 3 2 +2 )dx =3 x 1 + 5 x 2 4 +2x+c = 3 x + 5 4 x 2 +2x+c
(b)
x 2 ( x 5 +2x )dx = ( x 7 +2 x 3 )  dx = x 8 8 + 2 x 4 4 +c = x 8 8 + x 4 2 +c
(c)
3 x 4 +2x x 3 dx = ( 3 x 4 x 3 + 2x x 3 )  dx= ( 3x+2 x 2 )  dx = 3 x 2 2 2 x +c
(d)
(7+x)(7x) x 4 dx = ( 49 x 2 x 4 )  dx = ( 49 x 4 1 x 2 ) dx = ( 49 x 4 x 2 ) dx = 49 x 3 3 + 1 x +c = 49 3 x 3 + 1 x +c
(e)
(5x1) 3 dx = (5x1) 4 ( 4 )( 5 ) +c = 1 20 ( 5x1 ) 4 +c
(f)
3 ( 4x+7 ) 8 dx = 3 ( 4x+7 ) 8  dx = 3 ( 4x+7 ) 7 ( 7 )( 4 ) +c = 3 28 ( 4x+7 ) 7 +c