1 / | | /x\ | atan|-| dx | \2/ | / 0
Integral(atan(x/2), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Use integration by parts:
Let and let .
Then .
To find :
The integral of a constant is the constant times the variable of integration:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
So, the result is:
Now substitute back in:
Use integration by parts:
Let and let .
Then .
To find :
The integral of a constant is the constant times the variable of integration:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | / 2\ | /x\ | x | /x\ | atan|-| dx = C - log|1 + --| + x*atan|-| | \2/ \ 4 / \2/ | /
-log(5) + atan(1/2) + log(4)
=
-log(5) + atan(1/2) + log(4)
-log(5) + atan(1/2) + log(4)
Use the examples entering the upper and lower limits of integration.