Definite Intergrals. HELP!!

[arapp]

Find the definite integral of the following using a suitable substitution:

1) (x^2)/sqroot(x^3-1)dx

2) xe^(x^2)dx

3) (ln(x))^(7/2)/(x)dx

 

[galactus]

Find the definite integral of the following using a suitable substitution:

The substitutions are rather straightfroward. Nothing tricky.

1) \(\displaystyle \int \frac{x^{2}}{\sqrt{x^{3}-1}}dx\)

Use the sub \(\displaystyle u=x^{3}, \;\ \frac{du}{3}=x^{2}dx\)

2) \(\displaystyle \int xe^{x^{2}}dx\)

Use the sub \(\displaystyle u=x^{2}, \;\ \frac{du}{2}=xdx\)

3) \(\displaystyle \int\frac{(ln(x))^\frac{7}{2}}{x}dx\)

Let \(\displaystyle u=ln(x), \;\ du=\frac{1}{x}dx\)