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