Integrate ln(x)/x^4 using Integration by Parts | Homework Help

[duki]

Homework Statement

Integrate $$\int{\frac{lnx}{x^4}dx}$$

Homework Equations

The Attempt at a Solution

I get this:
$$u = ln x, du = \frac{1}{x}$$
$$dv=x^4, v=\frac{x^5}{5}dx$$
$$\frac{(lnx)x^5}{5}-\int{\frac{x^5}{5}*\frac{1}{x}dx} = \frac{(lnx)x^5}{5}-\frac{6x^6}{5}dx}$$


Am I doing this right?

 

[JG89]

Your dv should be the integral of 1/x^4, not x^4.

 

[duki]

Hmm, ok. So what would be v?

 

[JG89]

The integral of x^(-4), which is 1/-3 * x^-3

 

[duki]

Oooh, ok. Thanks for your help!