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

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

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

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

\frac{tan ^{2} ( \frac{x}{2} )}{2} + C

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = tan (\frac{x}{2})

= \frac{tan ^{2} ( \frac{x}{2} )}{2}

Add a constant to the solution

= \frac{tan ^{2} ( \frac{x}{2} )}{2} + C

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