# Thread: Need help with Definite Integrals

1. ## Need help with Definite Integrals

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

2. Originally Posted by arapp
Find the definite integral of the following using a suitable substitution:

you mean the antiderivative?

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

let u = x^3-1

2) xe^(x^2)dx

let u = x^2

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

let u = ln(x)
...

do it.

3. so what do I do from there??

4. Those would be indefinite integrals since your are not evaluating for any values.

My tip for substitution is always look at what part you can take the derivative of and it will replace something else in the function.

Ill show an example with the first.

$\int \frac{x^2}{\sqrt{x^3-1}} dx$

Notice we can take the following substitution

$u = x^3-1$

Taking the derivative of this yields.

$du = 3x^2 dx$

Now notice in the numerator there is an $x^2$ to replace it properly we simply get rid of the 3 in the derivative to make it fit properly

$\frac{1}{3}du = x^2 dx$

Now the numerator will be replaced properly when we do the substitution

$\frac{1}{3}\int \frac{1}{\sqrt{u}} du$

Now integrating this yields.

$\frac{2}{3} \cdot \sqrt{u}$

Now we substitute back into the answer

$\frac{2\sqrt{x^3-1}}{3}$

5. I'm still struggling with the last one can someone help

6. Originally Posted by arapp
I'm still struggling with the last one can someone help
$
u = \ln{x}
$

$
du = \frac{1}{x} \, dx
$

$
\int (\ln{x})^{\frac{7}{2}} \cdot \frac{1}{x} \, dx
$

see it now?