Question

INDEFINITE INTEGRATION.​

Answer 1

Answer:

( x + 1 ) ( x - 5 ) / 2  +  1 / ( x + 1 )  +  3 ln |x+1|  +  C

Step-by-step explanation:

Put u = x+1.  Then du = dx and

x³ = (u-1)³ = u³ - 3u² + 3u - 1.

So the integral becomes

∫ ( u - 3 + 3/u - 1/u² ) du

= u²/2 - 3u + 3 ln |u| + 1/u + C

= u ( u - 6 ) / 2 + 1/u + 3 ln |u| + C

= ( x + 1 ) ( x - 5 ) / 2  +  1 / ( x + 1 )  +  3 ln |x+1|  +  C