oo / | | 27 | cos (x) dx | / 2
Integral(cos(x)^27, (x, 2, oo))
Rewrite the integrand:
There are multiple ways to do this integral.
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 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 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 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 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:
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 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 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 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 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:
Now simplify:
Add the constant of integration:
The answer is:
/ | 19 15 7 23 3 27 25 5 21 9 17 | 27 11 13 715*sin (x) 572*sin (x) 286*sin (x) 78*sin (x) 13*sin (x) sin (x) 13*sin (x) 78*sin (x) 286*sin (x) 715*sin (x) 1287*sin (x) | cos (x) dx = C - 117*sin (x) + 132*sin (x) - ------------ - ------------ - ----------- - ----------- - ---------- - -------- + ----------- + ---------- + ------------ + ----------- + ------------- + sin(x) | 19 5 7 23 3 27 25 5 21 9 17 /
17 9 21 5 25 27 3 23 7 15 19 17 9 21 5 25 27 3 23 7 15 19 22308732928 13 11 1287*sin (2) 715*sin (2) 286*sin (2) 78*sin (2) 13*sin (2) sin (2) 13*sin (2) 78*sin (2) 286*sin (2) 572*sin (2) 715*sin (2) 22308732928 13 11 1287*sin (2) 715*sin (2) 286*sin (2) 78*sin (2) 13*sin (2) sin (2) 13*sin (2) 78*sin (2) 286*sin (2) 572*sin (2) 715*sin (2) <- ----------- - sin(2) - 132*sin (2) + 117*sin (2) - ------------- - ----------- - ------------ - ---------- - ----------- + -------- + ---------- + ----------- + ----------- + ------------ + ------------, ----------- - sin(2) - 132*sin (2) + 117*sin (2) - ------------- - ----------- - ------------ - ---------- - ----------- + -------- + ---------- + ----------- + ----------- + ------------ + ------------> 35102025 17 9 21 5 25 27 3 23 7 5 19 35102025 17 9 21 5 25 27 3 23 7 5 19
=
17 9 21 5 25 27 3 23 7 15 19 17 9 21 5 25 27 3 23 7 15 19 22308732928 13 11 1287*sin (2) 715*sin (2) 286*sin (2) 78*sin (2) 13*sin (2) sin (2) 13*sin (2) 78*sin (2) 286*sin (2) 572*sin (2) 715*sin (2) 22308732928 13 11 1287*sin (2) 715*sin (2) 286*sin (2) 78*sin (2) 13*sin (2) sin (2) 13*sin (2) 78*sin (2) 286*sin (2) 572*sin (2) 715*sin (2) <- ----------- - sin(2) - 132*sin (2) + 117*sin (2) - ------------- - ----------- - ------------ - ---------- - ----------- + -------- + ---------- + ----------- + ----------- + ------------ + ------------, ----------- - sin(2) - 132*sin (2) + 117*sin (2) - ------------- - ----------- - ------------ - ---------- - ----------- + -------- + ---------- + ----------- + ----------- + ------------ + ------------> 35102025 17 9 21 5 25 27 3 23 7 5 19 35102025 17 9 21 5 25 27 3 23 7 5 19
AccumBounds(-22308732928/35102025 - sin(2) - 132*sin(2)^13 + 117*sin(2)^11 - 1287*sin(2)^17/17 - 715*sin(2)^9/9 - 286*sin(2)^21/21 - 78*sin(2)^5/5 - 13*sin(2)^25/25 + sin(2)^27/27 + 13*sin(2)^3/3 + 78*sin(2)^23/23 + 286*sin(2)^7/7 + 572*sin(2)^15/5 + 715*sin(2)^19/19, 22308732928/35102025 - sin(2) - 132*sin(2)^13 + 117*sin(2)^11 - 1287*sin(2)^17/17 - 715*sin(2)^9/9 - 286*sin(2)^21/21 - 78*sin(2)^5/5 - 13*sin(2)^25/25 + sin(2)^27/27 + 13*sin(2)^3/3 + 78*sin(2)^23/23 + 286*sin(2)^7/7 + 572*sin(2)^15/5 + 715*sin(2)^19/19)
Use the examples entering the upper and lower limits of integration.