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

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

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

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

2 sinh (x) + C

Solution steps

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

Apply u-substitution

: \int 2 cosh (u) d u

= \int 2 cosh (u) d u

Take the constant out:

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

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

Use the common integral:

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

= 2 sinh (u)

Substitute back

u = x

= 2 sinh (x)

Add a constant to the solution

= 2 sinh (x) + C

\frac{4 - 4 s}{4 s ^{2} + 4 s + 17}

f (x) = sec (x) + tan (x)

\int 8 x - 4 d x

\int 4 sin^{3} (6 x co) s^{3} 6 x d x

\frac{d ^{2} y}{d t ^{2}} - 9 y = 0

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