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

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

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

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

- \frac{1}{sin ( x ) - 1} + C

Solution steps

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

Apply u-substitution

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

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = sin (x) - 1

= - \frac{1}{sin ( x ) - 1}

Add a constant to the solution

= - \frac{1}{sin ( x ) - 1} + C

\frac{\partial}{\partial x} (x^{2} + y^{2} (1 - x)^{3})

\frac{\partial}{\partial x} (\frac{x}{1 - x})

\int \frac{3 x - 4}{( x - 2 ) ( x ^{2} + 1 )} d x

\int \frac{x ^{2} - 16}{x - 4} d x

\int \frac{1}{5 - y} d y

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