What is the integral from 0 to x of sinh(3t) ?

The integral from 0 to x of sinh(3t) is 1/3 (cosh(3x)-1)

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integral from 0 to x of sinh(3t)

\int_{0}^{x} sinh (3 t) d t

\frac{1}{3} (cosh (3 x) - 1)

Solution steps

\int_{0}^{x} sinh (3 t) d t

Apply u-substitution

: \int_{0}^{3 x} sinh (u) \frac{1}{3} d u

= \int_{0}^{3 x} sinh (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{3 x} sinh (u) d u

Use the common integral:

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

= \frac{1}{3} [cosh (u)]_{0}^{3 x}

Compute the boundaries:

cosh (3 x) - 1

= \frac{1}{3} (cosh (3 x) - 1)

\int_{- 2}^{3} e^{\frac{- 4 x}{3}} d x

\int_{1}^{4} (\frac{x}{8} - \frac{3}{x}) d x

\int_{0}^{1} \frac{( - x + 1 ) ^{3}}{6} d x

\int_{1}^{3} h (x) d x

\int_{1}^{3} x e^{2 x} d x

What is the integral from 0 to x of sinh(3t) ?
The integral from 0 to x of sinh(3t) is 1/3 (cosh(3x)-1)