1 / | | 2 | cos (x) | ------- dx | tan(x) | / 0
Integral(cos(x)^2/tan(x), (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 times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of 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:
The integral of is .
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 times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of 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:
The integral of is .
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 times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of 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:
The integral of is .
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:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 2 / 2 \ / 2 \ | cos (x) 1 log\-1 + sec (x)/ log\sec (x)/ | ------- dx = C + --------- + ----------------- - ------------ | tan(x) 2 2 2 | 2*sec (x) /
Use the examples entering the upper and lower limits of integration.