What is the integral of (3sin(x))/((1+cos(x))^2) ?

The integral of (3sin(x))/((1+cos(x))^2) is 3/2 tan^2(x/2)+C

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integral of (3sin(x))/((1+cos(x))^2)

\int \frac{3 sin ( x )}{( 1 + cos ( x ) ) ^{2}} d x

\frac{3}{2} tan^{2} (\frac{x}{2}) + C

Solution steps

\int \frac{3 sin ( x )}{( 1 + cos ( x ) ) ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{sin ( x )}{( 1 + cos ( x ) ) ^{2}} d x

Apply u-substitution

: \int u d u

= 3 \cdot \int u d u

Apply the Power Rule

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

= 3 \cdot \frac{u ^{2}}{2}

Substitute back

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

= 3 \cdot \frac{tan ^{2} ( \frac{x}{2} )}{2}

Simplify

3 \cdot \frac{tan ^{2} ( \frac{x}{2} )}{2} : \frac{3}{2} tan^{2} (\frac{x}{2})

= \frac{3}{2} tan^{2} (\frac{x}{2})

Add a constant to the solution

= \frac{3}{2} tan^{2} (\frac{x}{2}) + C

\frac{d}{d x} ((ln (x)) (arctan (x)))

n = 1 \sum \infty \frac{2 ^{n}}{n 3 ^{n}}

\int \frac{24}{1 + 16 x ^{2}} d x

n = 0 \sum \infty (\frac{1}{2})^{n} x^{n}

\int \frac{2}{1 - 2 x} d x

What is the integral of (3sin(x))/((1+cos(x))^2) ?
The integral of (3sin(x))/((1+cos(x))^2) is 3/2 tan^2(x/2)+C