Question

what is the integral from (x/((2x^2)+1)) as x goes to 0 to 1 dx?
Could you show me step by step?

Answer 1

You want to use u-substitution. So u=2x^2+1
du=4xdx
(1/4)du=xdx
Replacing these in your integral gives:
\[\frac{1}{4}\int\limits \frac{du}{u}=\frac{1}{4}\ln|u|+C=\frac{1}{4}\ln|2x^2+1|+C\]

Answer 2

ok

Answer 3

You just need to plug your limits and get \(\frac{1}{4}[\ln(3)-\ln(1)]=\frac{1}{4}\ln(3)\).

Answer 4

thank you!