1 / | | sin(5*x)*cos(x)*1 dx | / 0
Integral(sin(5*x)*cos(x)*1, (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:
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
Rewrite the integrand:
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 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 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:
Add the constant of integration:
The answer is:
/ 2 6 | 4 5*cos (x) 8*sin (x) | sin(5*x)*cos(x)*1 dx = C - 5*sin (x) - --------- + --------- | 2 3 /
5 5*cos(1)*cos(5) sin(1)*sin(5) -- - --------------- - ------------- 24 24 24
=
5 5*cos(1)*cos(5) sin(1)*sin(5) -- - --------------- - ------------- 24 24 24
Use the examples entering the upper and lower limits of integration.