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

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

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integral of (sqrt(2x))/x

\int \frac{2 x}{x} d x

\frac{2}{x} x + 2 x + C

Solution steps

\int \frac{2 x}{x} d x

Simplify

\frac{2 x}{x} : \frac{2}{x}

= \int \frac{2}{x} d x

Apply Integration By Parts

: \frac{2}{x} x - \int - \frac{1}{2 x ^{\frac{1}{2}}} d x

= \frac{2}{x} x - \int - \frac{1}{2 x ^{\frac{1}{2}}} d x

\int - \frac{1}{2 x ^{\frac{1}{2}}} d x = - 2 x

= \frac{2}{x} x - (- 2 x)

Simplify

= \frac{2}{x} x + 2 x

Add a constant to the solution

= \frac{2}{x} x + 2 x + C

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

y = x^{3}, y = x^{2}

\frac{\partial}{\partial t} (t^{2} + 1)

f (x) = \frac{( x ^{2} )}{x - 5}

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

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