What is the integral of 5sinh(ln(2)-x/3) ?

The integral of 5sinh(ln(2)-x/3) is -15cosh(ln(2)-x/3)+C

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integral of 5sinh(ln(2)-x/3)

\int 5 sinh (ln (2) - \frac{x}{3}) d x

- 15 cosh (ln (2) - \frac{x}{3}) + C

Solution steps

\int 5 sinh (ln (2) - \frac{x}{3}) d x

Take the constant out:

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

= 5 \cdot \int sinh (ln (2) - \frac{x}{3}) d x

Apply u-substitution

= 5 \cdot \int - 3 sinh (u) d u

Take the constant out:

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

= 5 (- 3 \cdot \int sinh (u) d u)

Use the common integral:

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

= 5 (- 3 cosh (u))

Substitute back

u = ln (2) - \frac{x}{3}

= 5 (- 3 cosh (ln (2) - \frac{x}{3}))

Simplify

= - 15 cosh (ln (2) - \frac{x}{3})

Add a constant to the solution

= - 15 cosh (ln (2) - \frac{x}{3}) + C

What is the integral of 5sinh(ln(2)-x/3) ?
The integral of 5sinh(ln(2)-x/3) is -15cosh(ln(2)-x/3)+C