Question

integrate ln(4+x^2)dx

Answer 1

x(ln|x^2+4|-2) + 4arctan(x/2) + C

Answer 2

using integration by parts

Answer 3

let u = ln(4 +x^2) --->du = 2x/4+x^2
dv = dx ---> v = x. Replace everything into the formula you can have 2 parts. I just talk about the second part. which is \[\int\limits \frac{ 2x^2 }{ 4+x^2 }dx\]

Answer 4

make a long division to get \[\int\limits2 +\frac{ 8 }{ x^2+4 }\]

Answer 5

then, everything is easy.
Hope this help

Answer 6

yeah i was just stuck on the long division part
thanks!

Answer 7

Hi friend , I am sorry for the last part, It is negative , not positive, I mean -8/x^2+4. sorry for the mistake

Answer 8

oh okay thank you

Answer 9

you're welcome