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