What is the integral of (5cosh(sqrt(x)))/(sqrt(x)) ?

The integral of (5cosh(sqrt(x)))/(sqrt(x)) is 10sinh(sqrt(x))+C

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integral of (5cosh(sqrt(x)))/(sqrt(x))

\int \frac{5 cosh ( x )}{x} d x

10 sinh (x) + C

Solution steps

\int \frac{5 cosh ( x )}{x} d x

Take the constant out:

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

= 5 \cdot \int \frac{cosh ( x )}{x} d x

Apply u-substitution

: \int 2 cosh (u) d u

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

Use the common integral:

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

= 5 \cdot 2 sinh (u)

Substitute back

u = x

= 5 \cdot 2 sinh (x)

Simplify

= 10 sinh (x)

Add a constant to the solution

= 10 sinh (x) + C

n = 0 \sum \infty \frac{n}{2 n ^{2} + 1}

x \to 4 lim (\frac{7}{x - 5})

\frac{d}{d x} ((x^{2} - 5 x + 8) (3 x^{2} - 2))

\int \frac{5 x ^{2} + 7}{x \frac{4}{3}} d x

x \to 0 lim (sin (\frac{π}{2} - x))

What is the integral of (5cosh(sqrt(x)))/(sqrt(x)) ?
The integral of (5cosh(sqrt(x)))/(sqrt(x)) is 10sinh(sqrt(x))+C