Find the most general antiderivative of f(x) = (sinX / cos^2 X)?

Answer 1

alright. do this.
use substitution. put u=cos x and then du = -sin x dx

f(x) = -1/u^2 du and then just integrate that normally with the polynomial rule

f(x) = -u^-2 du
F(x) = u^-1 = 1/u
F(x) = 1/cos x + C

soooo that should be right

Answer 2

use substitution method to solve this problem.
lets say, a = cos x then da = - sin x da

substituting these two into the equation yields f(x) = -1a^-2
integrating f(x) with respect to a yields 1/a + constants

so the final results will be 1/cos x + constant (a = cos x)

Answer 3

write u = cos x, then your integral becomes

INT f(x) dx
= -INT du / u^2
= 1/u + C
= 1/cos x + C

(or, if you wish, = sec x + C)

Answer 4

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