1 / | | 2 | x*sec (x)*1 dx | / 0
Integral(x*sec(x)^2*1, (x, 0, 1))
Use integration by parts:
Let and let .
Then .
To find :
Now evaluate the sub-integral.
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 .
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | | 2 | x*sec (x)*1 dx = C + x*tan(x) + log(cos(x)) | /
log(cos(1)) + tan(1)
=
log(cos(1)) + tan(1)
Use the examples entering the upper and lower limits of integration.