Hi Everyone,

The integral of $\displaystyle \frac{1}{x^2}$ can be solved by applying the integration law onto $\displaystyle x^-2$ to get $\displaystyle \frac{-1}{x}$.

But if I try to solve this by Integration by Substitution, where $\displaystyle u=x^2$, I get the answer to be ;

$\displaystyle u=x^2$

$\displaystyle \frac{du}{dx} = 2x$

$\displaystyle dx = \frac{du}{2x}$

$\displaystyle \int\frac{1}{u} dx$

$\displaystyle \int\frac{1}{u} \frac{du}{2x}$

$\displaystyle \frac{1}{2x}\int\frac{1}{u} du$

$\displaystyle \frac{1}{2x} \cdot ln u$

$\displaystyle \frac{ln u}{2x}$

$\displaystyle \frac{ln x^2}{2x}$

But this is not equal to $\displaystyle \frac{-1}{x}$. Is it even possible to solve this $\displaystyle \int\frac{1}{x^2}$ by subsitution?

Sorry for bad layout, I will learn!

Thanks for Responses!

Roman