What is the integral of (sinh(e^{-x/2}))/(e^{x/2)} ?

The integral of (sinh(e^{-x/2}))/(e^{x/2)} is -2cosh(e^{-x/2})+C

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integral of (sinh(e^{-x/2}))/(e^{x/2)}

\int \frac{sinh ( e ^{- \frac{x}{2}} )}{e ^{\frac{x}{2}}} d x

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

Solution steps

\int \frac{sinh ( e ^{- \frac{x}{2}} )}{e ^{\frac{x}{2}}} d x

Apply u-substitution

= \int - 2 e^{u} sinh (e^{u}) d u

Take the constant out:

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

= - 2 \cdot \int e^{u} sinh (e^{u}) d u

Apply u-substitution

= - 2 \cdot \int sinh (v) d v

Use the common integral:

\int sinh (v) d v = cosh (v)

= - 2 cosh (v)

Substitute back

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

Add a constant to the solution

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

What is the integral of (sinh(e^{-x/2}))/(e^{x/2)} ?
The integral of (sinh(e^{-x/2}))/(e^{x/2)} is -2cosh(e^{-x/2})+C