What is the integral of 6sinh(x/2-ln(3)) ?

The integral of 6sinh(x/2-ln(3)) is 12cosh(x/2-ln(3))+C

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integral of 6sinh(x/2-ln(3))

\int 6 sinh (\frac{x}{2} - ln (3)) d x

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

Solution steps

\int 6 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

= 6 \cdot \int sinh (\frac{x}{2} - ln (3)) d x

Apply u-substitution

: \int sinh (u) \cdot 2 d u

= 6 \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

= 6 \cdot 2 \cdot \int sinh (u) d u

Use the common integral:

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

= 6 \cdot 2 cosh (u)

Substitute back

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

= 6 \cdot 2 cosh (\frac{x}{2} - ln (3))

Simplify

= 12 cosh (\frac{x}{2} - ln (3))

Add a constant to the solution

= 12 cosh (\frac{x}{2} - ln (3)) + C

y = e^{x}, y = 3, x = 0

5 e^{- x}

\int \frac{3 e ^{x}}{e ^{2 x} + 10 e ^{x} + 25} d x

\int \frac{( e ^{x} + 9 )}{( e ^{2 x} - 6 e ^{x} + 9 )} d x

f (x) = \frac{8}{x}, at x = 4

What is the integral of 6sinh(x/2-ln(3)) ?
The integral of 6sinh(x/2-ln(3)) is 12cosh(x/2-ln(3))+C