Homework Help: Calculus

Posted by Elaine on Wednesday, February 15, 2012 at 12:15am.

I have to use integration by parts to integrate tan^-1 (1/x)dx. I'm not sure what to use as u or dv. We were taught to use uv-integral of (vdu) to do this.

Calculus - Anonymous, Wednesday, February 15, 2012 at 11:06am
look for a u that does not get too messy on differentiation, and a v that can be integrated without too much troubls

here, it seems logical to use u = arctan(1/x) since we know we're going to get rid of the nasty arctan, and the chain rule will toss in a 1/x^2:

u = arctan(1/x)
du = 1/(1/x^2 + 1)* (-1/x^2) dx
= -1/(1+x^2) dx

dv = dx
v = x

uv-Int v*du = x*arctan(1/x) + Int(x/(1+x^2)) dx

Int v*du = 1/2 * ln(1+x^2)

So, the final answer is x*arctan(1/x) + 1/2 ln(1+x^2)

go ahead -- take the derivative and watch things cancel out!!

Answer this Question

Related Questions

calculus - Use integration by parts to evaluate the integral of x*sec^2(3x). My ...
Integral calculus - Please can anyone help with the following problems - thanks...
calculus-integration! - should i use substitution?? if yes how should should i ...
Integration - Intergrate ¡ì sec^3(x) dx could anybody please check ...
Calculus - "Evaluate the following indefinite integral using integration by...
Calculus - How do I integrate (x^2)(e^(x^3)) dx? I think it is integration by ...
calculus - How do I integrate x(arctanx) dx? Is it some sort of integration by ...
AP Calculus BC - Hi! Thank you very much for your help--- I'm not sure what ...
Math/Calculus - How would I integrate the following by parts: Integral of: (x^2...
CALCULUS - USE INTEGRATION BY PARTS TO FIND EACH INTEGRAL ƪx^5 Lnx dx

For Further Reading

First Name:
School Subject:
Answer: