1. ## integration

integral
2x^2(x^3+1)^(1/2) dx
Having the hardest time with this is there a simple way to do it.

2. Originally Posted by Nightasylum
integral
2x^2(x^3+1)^(1/2) dx
Having the hardest time with this is there a simple way to do it.
For $\displaystyle \int 2x^2 \sqrt{x^3+1}\,dx$ let $\displaystyle u = x^3+1$. See how that works?

3. Originally Posted by Nightasylum
integral
2x^2(x^3+1)^(1/2) dx
Having the hardest time with this is there a simple way to do it.
substitution ...

$\displaystyle u = x^3+1$

$\displaystyle du = 3x^2 \, dx$

$\displaystyle \frac{2}{3} \int 3x^2\sqrt{x^3+1} \, dx$

$\displaystyle \frac{2}{3} \int \sqrt{u} \, du$

finish ...

4. Originally Posted by skeeter
substitution ...

$\displaystyle u = x^3+1$

$\displaystyle du = 3x^2 \, dx$

$\displaystyle \frac{2}{3} \int 3x^2\sqrt{x^3+1} \, dx$

$\displaystyle \frac{2}{3} \int \sqrt{u} \, du$

finish ...
Ill get 2/3 (x^3+1)^3/2 + c But that doesnt work so im a little lost.

5. Originally Posted by Nightasylum
Ill get 2/3 (x^3+1)^3/2 + c But that doesnt work so im a little lost.
... you ignored the constant in front of the integral.

6. Originally Posted by skeeter
... you ignored the constant in front of the integral.
O ok I got it. Thanks a ton .