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Indefinte integral?
Whats the indefinite integral of
f(x)=(3-5cos^2(x)+cos(x)tan(x))/cos^2(x)
1 Answer
- hfshawLv 76 years ago
You want the integral of:
f(x)=(3-5cos^2(x)+cos(x)tan(x))/cos^2(x)
First, simplify the function
f(x) = 3*sec^2(x) - 5 + sec(x)*tan(x)
Note that the derivative of d(tan(x))/dx) = sec^2(x), and that the derivative of sec(x) = sec(x)*tan(x) so the integral of the first term on the right is 3*tan(x) and the integral of the last term is sec(x). . The integral of the second term, of course, is just -5*x.
Integral of {(3*sec^2(x) - 5 + sec(x)*tan(x)) dx} = 3*tan(x) + sec(x) - 5x + c
