1 / | | 5 2 | tan (x)*sec (x)*1 dx | / 0
Integral(tan(x)^5*sec(x)^2*1, (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
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:
The integral of is when :
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | 6 | 5 2 tan (x) | tan (x)*sec (x)*1 dx = C + ------- | 6 /
4 2 1 -1 - 3*cos (1) + 3*cos (1) - - - -------------------------- 6 6 6*cos (1)
=
4 2 1 -1 - 3*cos (1) + 3*cos (1) - - - -------------------------- 6 6 6*cos (1)
Use the examples entering the upper and lower limits of integration.