1 / | | sin(4*x)*cos(x) dx | / 0
Integral(sin(4*x)*cos(x), (x, 0, 1))
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.
Let .
Then let and substitute :
Integrate term-by-term:
The integral of is when :
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:
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 is when :
So, the result is:
Now substitute back in:
So, the result is:
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:
The result is:
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 is when :
So, the result is:
Now substitute back in:
So, the result is:
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:
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 when :
So, the result is:
Now substitute back in:
So, the result is:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ 5 3 | 8*cos (x) 4*cos (x) | sin(4*x)*cos(x) dx = C - --------- + --------- | 5 3 /
4 4*cos(1)*cos(4) sin(1)*sin(4) -- - --------------- - ------------- 15 15 15
=
4 4*cos(1)*cos(4) sin(1)*sin(4) -- - --------------- - ------------- 15 15 15
Use the examples entering the upper and lower limits of integration.