p - 4 / | | sin(2*x) | ----------- dx | 2 | 1 - sin (x) | / p - 6
Integral(sin(2*x)/(1 - sin(x)^2), (x, p/6, p/4))
There are multiple ways to do this integral.
Rewrite the integrand:
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 a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
Now substitute back in:
So, the result is:
So, the result is:
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 a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
Now substitute back in:
So, the result is:
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 :
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:
Now substitute back in:
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | sin(2*x) / 2 \ | ----------- dx = C - log\-1 + sin (x)/ | 2 | 1 - sin (x) | /
/ 2/p\\ / 2/p\\ - log|-1 + sin |-|| + log|-1 + sin |-|| \ \4// \ \6//
=
/ 2/p\\ / 2/p\\ - log|-1 + sin |-|| + log|-1 + sin |-|| \ \4// \ \6//
-log(-1 + sin(p/4)^2) + log(-1 + sin(p/6)^2)
Use the examples entering the upper and lower limits of integration.