1 / | | cos(x)*cos(4*x)*1 dx | / 0
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
There are multiple ways to do this integral.
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
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 is when :
Now substitute back in:
So, the result is:
The integral of cosine is sine:
The result is:
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
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 is when :
Now substitute back in:
So, the result is:
The integral of cosine is sine:
The result is:
So, the result is:
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 :
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 when :
So, the result is:
The result is:
Now substitute back in:
So, the result is:
The integral of cosine is sine:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ 3 5 | 8*sin (x) 8*sin (x) | cos(x)*cos(4*x)*1 dx = C - --------- + --------- + sin(x) | 3 5 /
cos(4)*sin(1) 4*cos(1)*sin(4) - ------------- + --------------- 15 15
=
cos(4)*sin(1) 4*cos(1)*sin(4) - ------------- + --------------- 15 15
Use the examples entering the upper and lower limits of integration.