# Need help with couple of integrals!

• June 1st 2010, 10:49 AM
goroner
Need help with couple of integrals!
i got some probs. to solve this integrals :

integral x*arctan(x)dx
integral (11x+7)/(2x^2+7x-4)dx
integral ln(x^2+1)dx
intgral e^x/(1-e^3x)dx

i tryed solving this but i get stucked somewhere the first one is with partial integration ,second one i substitute the denominator with u and i get 4x+7 for du and there i get stucked ,the third one is partial as well but again as the first one i get to a point where i need to solve integral x^2/(x^2+1) and this one is not rly simple i dont know to solve it so i need help there, the 4 one is also with sub. for u=e^x but then i get integral 1/1-u^3 i tryed to make sub. for t=1-u^3 so i can get one parameter in the denominator and two up and than devide in two integrals but i couldnt get it.. please some help if you know how to solve this , btw these are from faculty from exam sessions thanks! (Itwasntme)
• June 1st 2010, 10:55 AM
Faux Carnival
Hi, right now I'm in a hurry. But I'd like to give you a very useful tip. You can always use the Wolfram Online Integrator to solve integrals.

Wolfram Mathematica Online Integrator

And then go back from there. I mean, try to understand which method to use from the anti-derivative. Good luck!
• June 1st 2010, 10:59 AM
goroner
dude i tryed in mathematica it self i got it but i cant get till the result walking so it doesnt rly helped me even the online thingy is giving me the same result but it didnt help me i need some step by step solvation if anyone could do it thanks!
• June 1st 2010, 10:59 AM
harish21
Quote:

Originally Posted by goroner
i got some probs. to solve this integrals :

integral x*arctan(x)dx
integral (11x+7)/(2x^2+7x-4)dx
integral ln(x^2+1)dx
intgral e^x/(1-e^3x)dx

i tryed solving this but i get stucked somewhere the first one is with partial integration ,second one i substitute the denominator with u and i get 4x+7 for du and there i get stucked ,the third one is partial as well but again as the first one i get to a point where i need to solve integral x^2/(x^2+1) and this one is not rly simple i dont know to solve it so i need help there, the 4 one is also with sub. for u=e^x but then i get integral 1/1-u^3 i tryed to make sub. for t=1-u^3 so i can get one parameter in the denominator and two up and than devide in two integrals but i couldnt get it.. please some help if you know how to solve this , btw these are from faculty from exam sessions thanks! (Itwasntme)

1) use integration by parts:
$\int u \mbox{dv} = uv -\int v \mbox{du}$

where $u = arctan(x), dv = x dx$
$du = \frac{1}{x^{2}+1} dx, v = x^2/2:$
• June 1st 2010, 11:02 AM
harish21
Very few people might have the time to show step by step solutions to all 4 problems:

check here. Click on show steps.
• June 1st 2010, 11:03 AM
goroner
for the 1 one i did use partial integration and i get to a point to solve integral of x^2/(x^2+1) and here i get stucked i need help to solve that one
• June 1st 2010, 11:07 AM
goroner
says x^2/(x^2+1) should be done with long division but dont know to do that .. ehm =/
• June 1st 2010, 11:08 AM
harish21
integrate x&#x2a;arctan&#x28;x&#x29;dx - Wolfram|Alpha
Quote:

Originally Posted by goroner
for the 1 one i did use partial integration and i get to a point to solve integral of x^2/(x^2+1) and here i get stucked i need help to solve that one

• June 1st 2010, 11:18 AM
harish21
Quote:

Originally Posted by goroner
says x^2/(x^2+1) should be done with long division but dont know to do that .. ehm =/

You need to review your books/ notes:

$\frac{x^2}{x^{2}+1} = 1 - \frac{1}{x^2+1}$

Heard of partial fractions?

$\frac{x^2}{x^2+1} = A + \frac{B}{x^2+1}$

$x^2 = A(x^{2}+1) + B$

solving for A and B gives the required result.
• June 1st 2010, 11:32 AM
goroner
i did heard of partial fractions but i never solve one like this , mostly i was solving partial fractions with factors in the denominator ,anyways thanks for this a lot!