Question

Integral of (1/(x^3+x))dx?

Answer 1

partial fractions! :)

Answer 2

\[\frac{1}{x(x^2+1)}=\frac{A}{x}+\frac{Bx+C}{x^2+1}=\frac{A(x^2+1)+x(Bx+C)}{x(x^2+1)}\]
=>
\[1=Ax^2+Bx^2+Cx+A\]

Answer 3

\[=>1=A, A+B=0,C=0=>B=-1\]

Answer 4

\[ \int 1/(x^3+x) dx\]
\[ 1/(x^2+1)= 1/x- x/(x^2+1)\]

Answer 5

yep :)

Answer 6

integrate each term
\[\int 1/x = ln x\]
\[ \int x/(x^2+1)= 1/2 * ln( x^2+1)\]

Answer 7

Thanks.