Question

Please show how to integrate x/((1+x^2)^2)?

Answer 1

Try using integration by substitution, with u = x^2.

Answer 2

put x^2=t
then 2xdx=dt .. i.e. obtained by differentiating both sides of the equation wrt x.
=>xdx=dt/2
hence, integral of xdx/((1+x^2)^2) will become integral of dt/2((1+t)^2)=-1/(2(1+t))
substituting back x^2=t, we get the answer = -1/(2(1+x^2))

Answer 3

yeah..thank you

Answer 4

hey dude you have to use this:#1(1+x^2)=u
#2(2x)dx=du
#3(xdx)=du/2
#4 integ(x/((1+x^2)^2)=integ(du/2u^2)
then youre final answer:1/2(1+x^2)