MHB Indefinite integral with two parts

[find_the_fun]

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

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

I know I can't rewrite [math]e^{4\ln{x}}[/math] as [math]e^4e^\ln{x}[/math]

 

[Chris L T521]

Re: indefinite integral with two parts

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

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

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

Can you take things from here?

 

[find_the_fun]

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.