integration

**Nightasylum** · November 11th 2009, 03:49 PM

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

**Danny** · November 11th 2009, 03:51 PM

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 $\int 2x^2 \sqrt{x^3+1}\,dx$ let $u = x^3+1$ . See how that works?

**skeeter** · November 11th 2009, 03:53 PM

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 ...

$u = x^3+1$

$du = 3x^2 \, dx$

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

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

finish ...

**Nightasylum** · November 11th 2009, 03:57 PM

Originally Posted by skeeter

substitution ...

$u = x^3+1$

$du = 3x^2 \, dx$

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

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

finish ...

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

**skeeter** · November 11th 2009, 04:03 PM

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.

**Nightasylum** · November 11th 2009, 04:15 PM

Originally Posted by skeeter

... you ignored the constant in front of the integral.

O ok I got it. Thanks a ton .

Thread: integration