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

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

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

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

- cos (y) + y + C

Solution steps

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

Rewrite using trig identities

= \int sin (y) + 1 d y

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 (y) d y + \int 1 d y

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

\int 1 d y = y

= - cos (y) + y

Add a constant to the solution

= - cos (y) + y + C

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\int \frac{3 x - 2}{x ^{2} - 2 x + 5} d x

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