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

The integral of (5sin(sqrt(x)))/(sqrt(x)) is -10cos(sqrt(x))+C

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

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

- 10 cos (x) + C

Solution steps

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

Apply u-substitution

: \int 2 sin (u) d u

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

Use the common integral:

\int sin (u) d u = - cos (u)

= 5 \cdot 2 (- cos (u))

Substitute back

u = x

= 5 \cdot 2 (- cos (x))

Simplify

= - 10 cos (x)

Add a constant to the solution

= - 10 cos (x) + C

y^{^{'}} - \frac{2}{t} y = t^{3}

\int 20 + 75 e^{- \frac{t}{50}} d t

t \cdot cos (π \cdot t)

y^{^{'}} + 2 y = 3 sin (e^{2 x})

n = 1 \sum \infty \frac{( 2 ^{2 n} n ! )}{2 n + 1}

What is the integral of (5sin(sqrt(x)))/(sqrt(x)) ?
The integral of (5sin(sqrt(x)))/(sqrt(x)) is -10cos(sqrt(x))+C