What is the integral of (cos(sqrt(3x)))/(sqrt(x)) ?

The integral of (cos(sqrt(3x)))/(sqrt(x)) is 2/(sqrt(3))sin(sqrt(3)sqrt(x))+C

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integral of (cos(sqrt(3x)))/(sqrt(x))

\int \frac{cos ( 3 x )}{x} d x

\frac{2}{3} sin (3 x) + C

Solution steps

\int \frac{cos ( 3 x )}{x} d x

3 x = 3 x

= \int \frac{cos ( 3 x )}{x} d x

Apply u-substitution

: \int \frac{2 cos ( u )}{3} d u

= \int \frac{2 cos ( u )}{3} d u

Take the constant out:

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

= \frac{2}{3} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{3} sin (u)

Substitute back

u = 3 x

= \frac{2}{3} sin (3 x)

Add a constant to the solution

= \frac{2}{3} sin (3 x) + C

f (x) = \frac{x ^{2} + 1}{x ^{3} + 1}

f (x) = \frac{x + 6}{x + 1}

\frac{d}{d x} (20 t - \frac{1}{2} g (t, x) t^{2})

lo g_{e} (x)

\frac{d}{d x} (x^{2} e^{- x} + (ln (x))^{2})

What is the integral of (cos(sqrt(3x)))/(sqrt(x)) ?
The integral of (cos(sqrt(3x)))/(sqrt(x)) is 2/(sqrt(3))sin(sqrt(3)sqrt(x))+C