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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

\int - 4 x + 8 d x

\int \frac{x ^{2}}{x ^{2} + 36} d x

\int \frac{1}{4 x - 1} d x

\int e^{3 - 2 x} d x

2 x + 1

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