Question

intresting integral question
integral of x/[(1+x)(1+x^2)] from zero to infinity

Answer 1

\[\int\limits_{0}^{\infty}x \div[(1+x)(1+x^2)]\]

Answer 2

decomp the fraction?

Answer 3

what do you mean by decompose should i multiply both the terms in the denominator

Answer 4

\[\frac{x}{(1+x)(1+x^2)}=A\frac{1}{1+x}+(Bx+C)\frac{1}{1+x^2} \]
\[x=A(1+x^2)+(Bx+C)(1+x)\]
when x=-1, solve for A

Answer 5

i didi it i got A= -1/2, B=C=1/2

Answer 6

good, A is fine but ill trust you on BC

so the A part is a log, and the BC part i believe is also a log ... might split into a log and arctan

Answer 7

\[A\int \frac{1}{1+x}dx+B\int\frac{x}{1+x^2}dx+C\int \frac{1}{1+x^2}dx\]

Answer 8

ok got it but what about infinite as the limit i am getting log of infinite which is infinite so what about that

Answer 9

your limits (a to b) will most likely both have to be limited to 0 and inf, if they dont converge then the sum is infinity

Answer 10

the wolf says it converges ...