What is the integral of (3sinh(x))/((1+cosh(x))^2) ?

The integral of (3sinh(x))/((1+cosh(x))^2) is -3/(1+cosh(x))+C

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integral of (3sinh(x))/((1+cosh(x))^2)

\int \frac{3 sinh ( x )}{( 1 + cosh ( x ) ) ^{2}} d x

- \frac{3}{1 + cosh ( x )} + C

Solution steps

\int \frac{3 sinh ( x )}{( 1 + cosh ( 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{sinh ( x )}{( 1 + cosh ( x ) ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{( 1 + u ) ^{2}} d u

= 3 \cdot \int \frac{1}{( 1 + u ) ^{2}} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= 3 \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 3 (- \frac{1}{v})

Substitute back

= 3 (- \frac{1}{1 + cosh ( x )})

Simplify

3 (- \frac{1}{1 + cosh ( x )}) : - \frac{3}{1 + cosh ( x )}

= - \frac{3}{1 + cosh ( x )}

Add a constant to the solution

= - \frac{3}{1 + cosh ( x )} + C

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What is the integral of (3sinh(x))/((1+cosh(x))^2) ?
The integral of (3sinh(x))/((1+cosh(x))^2) is -3/(1+cosh(x))+C