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

\frac{e ^{x}}{2 x + 1}

y = x^{6} cos (x)

e^{x} (y^{3} + x y^{3} + 1) d x + 3 y^{2} (x e^{x} - 6) d y = 0

(- 7, 6), (9, - \frac{6}{7})

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