# Indefinite integral with two parts

#### find_the_fun

##### Active member
I'm trying to integrate $$\displaystyle \int e^{4\ln{x}}x^2 dx$$
I can't see using u-substition, $$\displaystyle x^2$$ isn't the derivative of $$\displaystyle e^{4\ln{x}}$$ nor vice-versa.

I tried integrating by parts and that didn't work. I used $$\displaystyle u=e^{4\ln{x}}$$ and $$\displaystyle dv=x^2 dx$$

I know I can't rewrite $$\displaystyle e^{4\ln{x}}$$ as $$\displaystyle e^4e^\ln{x}$$

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#### Chris L T521

##### Well-known member
Staff member
Re: indefinite integral with two parts

I'm trying to integrate $$\displaystyle \int e^{4\ln{x}}x^2 dx$$
I can't see using u-substition, $$\displaystyle x^2$$ isn't the derivative of $$\displaystyle e^{4\ln{x}}$$ nor vice-versa.

I tried integrating by parts and that didn't work. I used $$\displaystyle u=e^{4\ln{x}}$$ and $$\displaystyle dv=x^2 dx$$
Note that $e^{4\ln x} = e^{\ln(x^4)} = x^4$.

Can you take things from here?

#### find_the_fun

##### Active member
Re: indefinite integral with two parts

Note that $e^{4\ln x} = e^{\ln(x^4)} = x^4$.

Can you take things from here?
I guess the lesson learned from this is to simplify the expression algebraically before attempting integration techniques.