What is the integral of sinh(6x) ?

The integral of sinh(6x) is 1/6 cosh(6x)+C

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integral of sinh(6x)

\int sinh (6 x) d x

\frac{1}{6} cosh (6 x) + C

Solution steps

\int sinh (6 x) d x

Apply u-substitution

: \int sinh (u) \frac{1}{6} d u

= \int sinh (u) \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int sinh (u) d u

Use the common integral:

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

= \frac{1}{6} cosh (u)

Substitute back

u = 6 x

= \frac{1}{6} cosh (6 x)

Add a constant to the solution

= \frac{1}{6} cosh (6 x) + C

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\int 2 csc (x) d x

\frac{d}{d x} (b cos (x) + x^{2} sin (x))

y \to - 1 lim (y^{3} - 2 y^{2} + 3 y - 4)

\frac{1}{2} + \frac{1}{2} cos (2 t)