Expert: Paul Klarreich - 7/21/2009

Question
what is the integration of e^2x * cos-1 x

Answer
Questioner:   satish
Country:  India
Category:  Calculus
Private:  No
 
Subject:  integral calculus
Question:  what is the integration of e^2x * cos-1 x
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Hi, Satish,

Have you tried Integration by Parts yet?

Looks like:

{
| e^(2x) arccos(x) dx  = INTegral 1
}

Let  u = arccos x,  du = -1/sqrt(1-x^2) dx

dv = e^2x dx,   v = e^2x / 2

uv = 1/2 e^2x arccos x

-vdu = 1/2 e^2x / sqrt(..) = INT 2.

Now do it again:

Let u = 1/2 e^2x,  du = e^2x dx

dv = 1/sqrt(..) dx,  v = - arccos x

Now this leads back to the original, and the new 'uv' term cancels.
So I don't think there is a way to do this.