How do you find the indefinite integral of int x^2sqrt(x^3+3)dxx2x3+3dx?

1 Answer
Dec 7, 2016

The answer is =2/9(x^3+3)^(3/2)+C=29(x3+3)32+C

Explanation:

We use intx^ndx=x^(n+1)/(n+1)+C (n!=-1)xndx=xn+1n+1+C(n1)

Lets' do this by substitution

Let u=x^3+3u=x3+3

du=3x^2dxdu=3x2dx, =>, x^2dx=(du)/3x2dx=du3

Therefore,

intx^2sqrt(x^3+3)dxx2x3+3dx

=1/3intsqrtudu=13udu

=1/3intu^(1/2)du=13u12du

=1/3u^(3/2)/(3/2)=13u3232

=2/9u^(3/2)=29u32

=2/9(x^3+3)^(3/2)+C=29(x3+3)32+C