1. integrating by assumed knowledge

ok i've this question:

$\displaystyle \int \frac{3x^2}{\sqrt{1-x^6}}$

I know that the answer is $\displaystyle sin^-1(x^3) + c$

I see the relationship between $\displaystyle sin^-1(x)$ and $\displaystyle sin^-1(x^3)$ and their integrals and this question...But what would be the best method to use to integrate and if it is substitution, what will u equal?

2. Originally Posted by tsal15
ok i've this question:

$\displaystyle \int \frac{3x^2}{\sqrt{1-x^6}}$

I know that the answer is $\displaystyle sin^-1(x^3) + c$

I see the relationship between $\displaystyle sin^-1(x)$ and $\displaystyle sin^-1(x^3)$ and their integrals and this question...But what would be the best method to use to integrate and if it is substitution, what will u equal?

Substitute $\displaystyle u = x^3 \Rightarrow dx = \frac{du}{3x^2}$.
Substitute $\displaystyle u = x^3 \Rightarrow dx = \frac{1}{3x^2}$.
Actually if $\displaystyle \frac{du}{dx} = 3x^2$ then $\displaystyle dx = \frac{du}{3x^2}$.
Actually if $\displaystyle \frac{du}{dx} = 3x^2$ then $\displaystyle dx = \frac{du}{3x^2}$.