1 / | | x*acot(x) | --------- dx | 2 | / 0
Integral(x*acot(x)/2, (x, 0, 1))
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 is when :
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
The integral of a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
The result is:
So, the result is:
So, the result is:
Add the constant of integration:
The answer is:
/ | 2 | x*acot(x) atan(x) x x *acot(x) | --------- dx = C - ------- + - + ---------- | 2 4 4 4 | /
Use the examples entering the upper and lower limits of integration.