1 / | | 5 | cos (x) dx | / 0
Integral(cos(x)^5, (x, 0, 1))
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:
Add the constant of integration:
The answer is:
/ | 3 5 | 5 2*sin (x) sin (x) | cos (x) dx = C - --------- + ------- + sin(x) | 3 5 /
3 5 2*sin (1) sin (1) - --------- + ------- + sin(1) 3 5
=
3 5 2*sin (1) sin (1) - --------- + ------- + sin(1) 3 5
-2*sin(1)^3/3 + sin(1)^5/5 + sin(1)
Use the examples entering the upper and lower limits of integration.