Integrating Fractions: A Comprehensive Guide

[Lodve]

I really struggle to integrate this fraction expression:


$$\int \frac{2}{4x^2+1}$$

 

[Chewy0087]

I presume you're familiar with the standard table of integrals?

http://www.maths.abdn.ac.uk/~igc/tch/ma1002/int/node51.html

Here's a list of many common ones, see if you can get it into the right form for one of them.

If you have to work this out by hand, consider using a trigonometric substitution, but choose carefully.

(Hint: the relationship 1 + x^2 = sec^2 for x = tan x)

 

[Lodve]

Yes, I'm fimiliar with some the of standard table of integrals. I think I just change the equation above in the form
$$\int \frac{1}{x^2+a^2}$$ where a is an integer, so that the integration of the equation would likely be
$$\frac{1}{a} arctan(x/a)$$

But I'm not sure if I've done it right.

 

[Chewy0087]

You chose the right one, try to get it into a form like that.

 

[Lodve]

Thank you for helping me :D