1 / | | 3 | cot (x) dx | / 0
Integral(cot(x)^3, (x, 0, 1))
Rewrite the integrand:
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:
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:
Now substitute back in:
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
The result is:
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ | / 2 \ 2 | 3 log\csc (x)/ csc (x) | cot (x) dx = C + ------------ - ------- | 2 2 /
Use the examples entering the upper and lower limits of integration.