Question

whats the integral of ln(x^(2) + 1)??

Answer 1

so far I have:\[\ln(x ^{2}+1)x-\int\limits_{}^{}x*\frac{ 2x }{ x ^{2}+1 } dx\]

Answer 2

Long division for the int. by parts?

Answer 3

uhmm could that work?

Answer 4

my guess is parts

Answer 5

oh nvm you have that already

Answer 6

\[\ln(x ^{2}+1)x-\int\limits\limits_{}^{}2-\frac{2}{x^2+1} dx \]

Answer 7

\[\frac{x^2}{x^2+1}=\frac{x^2+1}{x^2+1}-\frac{1}{x^2+1}=1-\frac{1}{x^2+1}\]

Answer 8

first integral is obvious, second part is the derivative of arctangent

Answer 9

i ignored the 2, @.Sam. has it

Answer 10

you could divide too, but i find that gimmick easier than long division

Answer 11

thank you! I'll try and post it when im done :P