Math Help - Integral Method using the Substitution Method

1. Integral Method using the Substitution Method

Hey There,
I am doing a question and I can solve it the antiderivative way, but I can't seem to come up with the substitution method.
3 + x^3/2 dx
__ _____ divide by
x^3 3

So I put the integral sign 3x^-3 - 3x^3/2 dx
now do I take out a 3 and have 3(x^-3-3x^3/2) dx or NO??

I can't figure out the U and du.

Any help would be great, thanks.

2. Re: Integral Method using the Substitution Method

$\displaystyle \int \dfrac{3 + \dfrac{x^3}{2} }{ 3 x^3} \, dx$

3. Re: Integral Method using the Substitution Method

$\int \left(\frac{3}{x^3} + \frac{x^{\frac{3}{2}}}{3}\right)\,dx$
We have: . $\int\left(3x^{-3} + \tfrac{1}{3}x^{\frac{3}{2}}\right)\,dx$
. . . . . . $=\;\frac{3x^{-2}}{-2} + \frac{\frac{1}{3}x^{\frac{5}{2}}}{\frac{5}{2}} + C$
. . . . . . $=\;-\frac{3}{2x^2} + \frac{2}{15}x^{\frac{5}{2}} + C$