# Evaluate the integrals : 3x^2 sqr(x^3+1)dx?

##### 1 Answer

May 27, 2018

#### Explanation:

We want to solve

#I=int3x^2sqrt(x^3+1)dx#

Make a substitution

#I=intsqrt(u)du=intu^(1/2)du#

By the power rule for integration

#I=u^(1/2+1)/(1/2+1)+C=u^(3/2)/(3/2)+C=2/3u^(3/2)+C#

Substitute back

#I=2/3(x^3+1)^(3/2)+C#