1 / | | / 1 \ | |sin(2*x) + ----------| dx | \ sin(2*x)*3/ | / 0
Integral(sin(2*x) + 1/(sin(2*x)*3), (x, 0, 1))
Integrate term-by-term:
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:
The integral of sine is negative cosine:
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:
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:
The integral of is when :
So, the result is:
Now substitute back in:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
So, the result is:
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | / 1 \ cos(2*x) log(1 + cos(2*x)) log(-1 + cos(2*x)) | |sin(2*x) + ----------| dx = C - -------- - ----------------- + ------------------ | \ sin(2*x)*3/ 2 12 12 | /
pi*I oo + ---- 12
=
pi*I oo + ---- 12
oo + pi*i/12
Use the examples entering the upper and lower limits of integration.