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

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

Popular >

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

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

- \frac{1}{2 ( 1 + cosh ( x ) ) ^{2}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{( 1 + u ) ^{3}} d u

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

Apply u-substitution

: \int \frac{1}{v ^{3}} d v

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

Apply the Power Rule

: - \frac{1}{2 v ^{2}}

= - \frac{1}{2 v ^{2}}

Substitute back

= - \frac{1}{2 ( 1 + cosh ( x ) ) ^{2}}

Add a constant to the solution

= - \frac{1}{2 ( 1 + cosh ( x ) ) ^{2}} + C

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

\int \frac{1}{9 x + x ln ^{2} ( x )} d x

\int \frac{( x + 5 )}{( x ^{2} - 6 x - 15 )} d x

\int \frac{sec ^{4} ( θ )}{tan ^{5} ( θ )} d θ

\int \frac{130}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

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