What is the integral of (cos(θ))/(sqrt(1-sin(θ))) ?

The integral of (cos(θ))/(sqrt(1-sin(θ))) is -2sqrt(1-sin(θ))+C

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integral of (cos(θ))/(sqrt(1-sin(θ)))

\int \frac{cos ( θ )}{1 - sin ( θ )} d θ

- 2 1 - sin (θ) + C

Solution steps

\int \frac{cos ( θ )}{1 - sin ( θ )} d θ

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - 2 u^{\frac{1}{2}}

Substitute back

u = 1 - sin (θ)

= - 2 (1 - sin (θ))^{\frac{1}{2}}

Apply radical rule:

= - 2 1 - sin (θ)

Add a constant to the solution

= - 2 1 - sin (θ) + C

y = 6 ln (x^{2}), (e, 12)

f (x) = e^{x} sin (x), (0, 0)

y = \frac{3 + 7 x - 8 x}{x}

(x^{2} e^{x + 3})^{^{'}}

y^{^{'}} = - 3 y + e^{- 2 x}, y (0) = 0

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