Question

Find the integral of 1/((x+1)(x^2+1)) dx.

Answer 1

Have you learnt partial fractions?

Answer 2

Yes, but this one is weird.

Answer 3

Why?

Answer 4

Because x^2+1 doesn't have real roots.

Answer 5

Then treat it as one entity

Answer 6

resolve into partial fractions and integate

Answer 7

can you show the partial fractions?

Answer 8

\[\frac{ 1 }{ \left( x+1 \right)\left( x^2+1 \right) }=\frac{ A }{ x+1 }+\frac{ Bx+C }{ x^2+1 }\]
can you proceed further?

Answer 9

This result would be useful: http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=d%2Fdx%20tan%5E-1(x)

Answer 10

\[1=A(x^2+1)+(Bx+C)(x+1)\]
\[1=A(x^2+1)+Bx^2+Bx+Cx+C\]
Equate the coefficients of x^2,x and constant terms

Answer 11

0=A+B
0=B+C
1=A+C
find A,B,C
and then integrate.