Question

evaluate the integral fro 0 to 2 x/(1+x^2)dx

Answer 1

make the substitution
\[u=1+x^2\] giving \[du=2xdx\]

Answer 2

might as well change the limits of integration while we are at is so we don't have to change back.

Answer 3

\[u(0)=1\]
\[u(2)=5\] now the integral is
\[\int_1^5\frac{1}{u}du\]

Answer 4

sorry i forgot to divide by 2

Answer 5

\[u=1+x^2\]
\[du=2xdx\]
\[du=\frac{dx}{2}\] integral is
\[\frac{1}{2}\int_1^5\frac{1}{u}du\]

Answer 6

anti-derivative of
\[\frac{1}{u}=ln(u)\]
get
\[\frac{1}{2}(\ln(5)-\ln(1))=\frac{1}{2}\ln(5)\]

Answer 7

why u use ln(5)-ln(1).. i dont know how to work with that