What is the integral of (sin(x))/(2sqrt(x)) ?

The integral of (sin(x))/(2sqrt(x)) is sqrt(pi/2)\S(sqrt(2/pi)sqrt(x))+C

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integral of (sin(x))/(2sqrt(x))

\int \frac{sin ( x )}{2 x} d x

\frac{π}{2} § (\frac{2}{π} x) + C

Solution steps

\int \frac{sin ( x )}{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{sin ( x )}{x} d x

Apply u-substitution

: \int 2 sin (u^{2}) d u

= \frac{1}{2} \cdot \int 2 sin (u^{2}) d u

Take the constant out:

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

= \frac{1}{2} \cdot 2 \cdot \int sin (u^{2}) d u

Use the nonelementary integral:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= \frac{1}{2} \cdot 2 \frac{π}{2} § (\frac{2}{π} u)

Substitute back

u = x

= \frac{1}{2} \cdot 2 \frac{π}{2} § (\frac{2}{π} x)

Simplify

\frac{1}{2} \cdot 2 \frac{π}{2} § (\frac{2}{π} x) : \frac{π}{2} § (\frac{2}{π} x)

= \frac{π}{2} § (\frac{2}{π} x)

Add a constant to the solution

= \frac{π}{2} § (\frac{2}{π} x) + C

0.7 x^{3}

x \to 0 lim (\frac{sin ( x + π )}{x})

\frac{d y}{d x} = - \frac{1 + y ^{2}}{1 + x ^{2}}

\frac{d}{d t} (1 - 2 cos (t))

\int \frac{8 x + 9}{( x ^{2} + 9 ) ( 8 - x )} d x

What is the integral of (sin(x))/(2sqrt(x)) ?
The integral of (sin(x))/(2sqrt(x)) is sqrt(pi/2)\S(sqrt(2/pi)sqrt(x))+C