Thursday

January 29, 2015

January 29, 2015

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

- Calculus -
**Anonymous**, Wednesday, February 15, 2012 at 11:06amlook 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-integration! - should i use substitution?? if yes how should should i ...

calculus - Use integration by parts to evaluate the integral of x*sec^2(3x). My ...

Calculus - Integration - Hello! I really don't think I am understanding my calc ...

calculus-integration - integrate -2/xln^4(x)...plz help me..give me an idea on ...

Math/Calculus - How would I integrate the following by parts: Integral of: (x^2...

calc - evaluate the integral: y lny dy i know it's integration by parts but i ...

Calculus II - Integrate using integration by parts (integral) (5-x) e^3x u = 5-x...

calc - also: integral of tan^(-1)y dy how is integration of parts used in that? ...

Calculus - "Evaluate the following indefinite integral using integration by ...

Calculus - Use integration by parts to evaluate the integral xsqrt(2x+6)dx.