Integration? - Math

[Asjad]

I guess this question fits here, right then, I am stuck with pure mathematics, how the hell am I supposed to integrate lnx/x^2 ??? ive spent hours and hours it just doesn't integrate right!

Ive been using integration by parts, which is required by the question

INT u dv/dx dx = uv - INT v du/dx dx

[Christopher]

Sure, here we go:

So you have f(x) = ln(x)x^-2

Let u = ln(x)

So, du/dx = x^-1
Thus, du = x^-1 dx

Now, let dv/dx = x^-2

Therefore, integrate dv/dx to get v = -x^-1

Now for integration by parts:

INT u.dv = uv - INT v.du -Sub in the above results.

= ln(x).-x^-1 - INT -x^-1 . x^-1 . dx
= ln(x).-x^-1 - INT -x^-2 . dx
= ln(x).-x^-1 - x^-1 + C - But lets just ignore the constant C.
= ln(x).-x^-1 - x^-1

Therefore, INT u.dv = ln(x).-x^-1 - x^-1 = -x^-1(ln(x)+1)

Hope that helps.

[machf]

I had thought this would be a question regarding numerical integration and computers, given the section where it was being asked... turned out to be simple mathematical integration instead.

[Shadow Wolf]

thanks god I gave up maths after my GCSEs

[Asjad]

Hey thanks Chris! I had figured out how to do this, iam still learning to integrate by parts, turned out i wasn't using the formula properly. But thanks again! Iam sure of the way to use the formula now.

[Second Illiteration]

This makes me miss math

[Slugger]

Everyone's favorite integral:

INT sqrt(tanx)dx