What is the integral of (4sin(x))/((1+cos(x))^2) ?

The integral of (4sin(x))/((1+cos(x))^2) is 2tan^2(x/2)+C

Popular >

integral of (4sin(x))/((1+cos(x))^2)

\int \frac{4 sin ( x )}{( 1 + cos ( x ) ) ^{2}} d x

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

Solution steps

\int \frac{4 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

= 4 \cdot \int \frac{sin ( x )}{( 1 + cos ( x ) ) ^{2}} d x

Apply u-substitution

: \int u d u

= 4 \cdot \int u d u

Apply the Power Rule

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

= 4 \cdot \frac{u ^{2}}{2}

Substitute back

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

= 4 \cdot \frac{tan ^{2} ( \frac{x}{2} )}{2}

Simplify

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

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

Add a constant to the solution

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

f (x) = x^{2} - \frac{1}{x}, at (- 1)

\int \frac{( 2 x + 7 )}{2 x ^{2} + 2 x + 1} d x

\int cos (2) x^{2} d x

f (x) = \frac{7}{x}, at x = 6

y^{^{'}} = \frac{e ^{x} - e ^{y}}{1 + e ^{x}}

What is the integral of (4sin(x))/((1+cos(x))^2) ?
The integral of (4sin(x))/((1+cos(x))^2) is 2tan^2(x/2)+C