1. ## Difficult Integral

I was wondering whether anyone there could explain how to integrate (e^x)/(1+x^2) by parts.

Many Thanks

dz

2. Not sure how parts will help here

Wolfram Mathematica Online Integrator

3. By parts doesn't seem to work here

4. This is all wrong

Originally Posted by harish21
I used integration by parts this way:

Let $u= 1+{x^2} ; v = e^x$

Then $du= 2x dx ; dv = e^x$

So, $uv - \int v.du$

= $(1+{x^2})(e^x) - \int e^x 2x dx$

= $(1+{x^2})(e^x) - 2e^{x}(x-1)$

For parts you need to make one variable u' and the other v in your case

Should it not be??

Let ${\color{red}u'= \frac{1}{1+{x^2}}} , v = e^x$

Then $u= \tan^{-1}x , v' = e^x$

Still this will not reduce.

5. I agree Pickslides. I tried solving this one using a Matematica powered calculator and it gives me a solution with irrational numbers. Yet I sense that this is not right...

Here it is: