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

The integral of 5sinh(x/2-ln(3)) is 10cosh(x/2-ln(3))+C

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

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

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

Solution steps

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

Apply u-substitution

= 5 \cdot \int sinh (u) \cdot 2 d u

Take the constant out:

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

= 5 \cdot 2 \cdot \int sinh (u) d u

Use the common integral:

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

= 5 \cdot 2 cosh (u)

Substitute back

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

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

Simplify

= 10 cosh (\frac{x}{2} - ln (3))

Add a constant to the solution

= 10 cosh (\frac{x}{2} - ln (3)) + C

What is the integral of 5sinh(x/2-ln(3)) ?
The integral of 5sinh(x/2-ln(3)) is 10cosh(x/2-ln(3))+C