pi -- 4 / | | / 1 2 \ | |------- + 4*cos (x)| dx | | 2 | | \sin (x) / | / 0
Integral(1/(sin(x)^2) + 4*cos(x)^2, (x, 0, pi/4))
Integrate term-by-term:
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 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 cosine is sine:
So, the result is:
Now substitute back in:
So, the result is:
The integral of a constant is the constant times the variable of integration:
The result is:
So, the result is:
Don't know the steps in finding this integral.
But the integral is
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | / 1 2 \ cos(x) | |------- + 4*cos (x)| dx = C + 2*x - ------ + sin(2*x) | | 2 | sin(x) | \sin (x) / | /
Use the examples entering the upper and lower limits of integration.