1 / | | cos(2*x)*cos(7*x) 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 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 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 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 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:
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 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:
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:
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:
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 a constant times a function is the constant times the integral of the function:
The integral of cosine is sine:
So, the result is:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ 3 5 9 | 7 26*sin (x) 128*sin (x) 128*sin (x) | cos(2*x)*cos(7*x) dx = C - 32*sin (x) - ---------- + ----------- + ----------- + sin(x) | 3 5 9 /
2*cos(7)*sin(2) 7*cos(2)*sin(7) - --------------- + --------------- 45 45
=
2*cos(7)*sin(2) 7*cos(2)*sin(7) - --------------- + --------------- 45 45
Use the examples entering the upper and lower limits of integration.