Math Integration Question

[us3rnotfound]

integral(4x/(2 + x^2))dx

The answer is 2log(2 + x^2), but how do you arrive at this? Partial fractions, Integration by parts?

 

[slackwarelinux]

let u = 2 + x^2
du = 2x dx
so, you get int(2du/u)
which is 2ln(u) which is 2ln(2 + x^2)

 

[us3rnotfound]

Oh awesome dude ty

 

[StevenYoo]

the log in this case is the natural log, ln.

use substitution to solve it:

n = 2 + x^2
dn = 2x dx

therefore the integral can be written:

2 * integral (dn/n)

which is:

2 * ln n

or

2ln(2 + x^2)

*EDIT* too slow!