What is the integral of sinh(sqrt(x)) ?

The integral of sinh(sqrt(x)) is 2(sqrt(x)cosh(sqrt(x))-sinh(sqrt(x)))+C

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integral of sinh(sqrt(x))

\int sinh (x) d x

2 (x cosh (x) - sinh (x)) + C

Solution steps

\int sinh (x) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply Integration By Parts

: u cosh (u) - \int cosh (u) d u

= 2 (u cosh (u) - \int cosh (u) d u)

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

= 2 (u cosh (u) - sinh (u))

Substitute back

u = x

= 2 (x cosh (x) - sinh (x))

Add a constant to the solution

= 2 (x cosh (x) - sinh (x)) + C

\frac{d}{d x} ((\frac{x ^{2}}{x ^{3} - 4 x})^{3})

\frac{d}{d x} (\frac{x ^{n}}{n !})

\int_{0}^{π} sin^{4} (2 x) d x

x \to - \infty lim (x \cdot e^{x})

\frac{d}{d y} (sin^{2} (y))

What is the integral of sinh(sqrt(x)) ?
The integral of sinh(sqrt(x)) is 2(sqrt(x)cosh(sqrt(x))-sinh(sqrt(x)))+C