What is the integral of 1/(sqrt(x))sin(sqrt(x)) ?

The integral of 1/(sqrt(x))sin(sqrt(x)) is -2cos(sqrt(x))+C

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integral of 1/(sqrt(x))sin(sqrt(x))

\int \frac{1}{x} sin (x) d x

- 2 cos (x) + C

Solution steps

\int \frac{1}{x} sin (x) d x

Apply u-substitution

: \int 2 sin (u) d u

= \int 2 sin (u) d u

Take the constant out:

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

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

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = x

= 2 (- cos (x))

Simplify

= - 2 cos (x)

Add a constant to the solution

= - 2 cos (x) + C

\int \frac{x}{( x ^{2} + 1 ) ( x ^{2} + 4 )} d x

\int (1 + 0.5 t) e^{- 0.004 t} d t

\frac{\partial}{\partial x} (5 x^{2} - 2 y)

\int (x^{\frac{3}{2}} + 8 x + 9) d x

f (x) = - 3 x^{2} + 6 x + 4, at x = 1

What is the integral of 1/(sqrt(x))sin(sqrt(x)) ?
The integral of 1/(sqrt(x))sin(sqrt(x)) is -2cos(sqrt(x))+C