What is the integral of (8cosh(sqrt(x)))/(sqrt(x)) ?

The integral of (8cosh(sqrt(x)))/(sqrt(x)) is 16sinh(sqrt(x))+C

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integral of (8cosh(sqrt(x)))/(sqrt(x))

\int \frac{8 cosh ( x )}{x} d x

16 sinh (x) + C

Solution steps

\int \frac{8 cosh ( x )}{x} d x

Take the constant out:

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

= 8 \cdot \int \frac{cosh ( x )}{x} d x

Apply u-substitution

: \int 2 cosh (u) d u

= 8 \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

= 8 \cdot 2 \cdot \int cosh (u) d u

Use the common integral:

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

= 8 \cdot 2 sinh (u)

Substitute back

u = x

= 8 \cdot 2 sinh (x)

Simplify

= 16 sinh (x)

Add a constant to the solution

= 16 sinh (x) + C

\int \frac{( 5 - x )}{2 x ^{2} + x - 1} d x

x \to 0 lim (\frac{( 4 ^{2 x} - 1 )}{( 4 ^{x} - 1 )})

z \to 2 lim (\frac{z ^{2} + 3}{i z})

ln (1 + 7 x)

\frac{d ^{2}}{d x ^{2}} (4 x + 15)

What is the integral of (8cosh(sqrt(x)))/(sqrt(x)) ?
The integral of (8cosh(sqrt(x)))/(sqrt(x)) is 16sinh(sqrt(x))+C