1 / | | log(atan(x)) | ------------ dx | 2 | 1 + x | / 0
Integral(log(atan(x))/(1 + x^2), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
Use integration by parts:
Let and let .
Then .
To find :
The integral of the exponential function is itself.
Now evaluate the sub-integral.
The integral of the exponential function is itself.
Now substitute back in:
Use integration by parts:
Let and let .
Then .
To find :
The integral of is .
Now evaluate the sub-integral.
The integral of is .
Now simplify:
Add the constant of integration:
The answer is:
/ | | log(atan(x)) | ------------ dx = C - atan(x) + atan(x)*log(atan(x)) | 2 | 1 + x | /
/pi\ pi*log|--| pi \4 / - -- + ---------- 4 4
=
/pi\ pi*log|--| pi \4 / - -- + ---------- 4 4
Use the examples entering the upper and lower limits of integration.