What is the integral of (cos^2(x))/(1-sin(x)) ?

The integral of (cos^2(x))/(1-sin(x)) is -cos(x)+x+C

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integral of (cos^2(x))/(1-sin(x))

\int \frac{cos ^{2} ( x )}{1 - sin ( x )} d x

- cos (x) + x + C

Solution steps

\int \frac{cos ^{2} ( x )}{1 - sin ( x )} d x

Rewrite using trig identities

= \int sin (x) + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (x) d x + \int 1 d x

\int sin (x) d x = - cos (x)

\int 1 d x = x

= - cos (x) + x

Add a constant to the solution

= - cos (x) + x + C

x \to 2 lim (9 x)

5 x + 6, at x = 2

y = e^{3 x}, at x = \frac{1}{3} ln (3)

y (x + 1) + \frac{d y}{d x} = 0

6 - x^{2}

What is the integral of (cos^2(x))/(1-sin(x)) ?
The integral of (cos^2(x))/(1-sin(x)) is -cos(x)+x+C