# Math Help - Do I have to use Integration by Parts for this?

1. ## Do I have to use Integration by Parts for this?

\int 2^3ln(x)dx

What I did:

u = ln(x) v = 2x^4/4
du = 1/x dv = 2x^3*dx

Then it becomes: \int ln(x)(2x^4/4) - \int (2x^4/4x)

Next from \int (2x^4/4x)

u = 1/x v = x^5/10
du = -1/x^2 dv = 2x^4/4

Thus becoming: (1/x)(2x^4/4)dx - \int x^5/10(-1/x^2)

At this point it does not seem to be right because my teachers answer is x^4/(4ln(x) - 1)

Can someone help me please? I have a test tomorrow and I need to know ASAP.

2. Your u du v and dv are all correct

Remember the formula for integration by parts is

$\int udv=uv-\int vdu$

So plugging in your info above I get

$\frac{x^4\ln(x)}{2}-\frac{1}{2}\int x^3dx$

You do not need integration by parts just use the power rule!

3. I figured it out, thanks!