1 / | | 1 + sin(x) | ---------- dx | 1 + cos(x) | / 0
Integral((1 + sin(x))/(1 + cos(x)), (x, 0, 1))
Rewrite the integrand:
Integrate term-by-term:
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:
Don't know the steps in finding this integral.
But the integral is
The result is:
Add the constant of integration:
The answer is:
/ | | 1 + sin(x) /x\ | ---------- dx = C - log(1 + cos(x)) + tan|-| | 1 + cos(x) \2/ | /
/ 2 \ log\1 + tan (1/2)/ + tan(1/2)
=
/ 2 \ log\1 + tan (1/2)/ + tan(1/2)
log(1 + tan(1/2)^2) + tan(1/2)
Use the examples entering the upper and lower limits of integration.