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