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

The integral of ((ln(x))/(sqrt(x^3))) is -(2ln(x))/(sqrt(x))-4/(sqrt(x))+C

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integral of ((ln(x))/(sqrt(x^3)))

\int (\frac{ln ( x )}{x ^{3}}) d x

- \frac{2 ln ( x )}{x} - \frac{4}{x} + C

Solution steps

\int \frac{ln ( x )}{x ^{3}} d x

x^{3} = x^{\frac{3}{2}},

assuming

x \geq 0

= \int \frac{ln ( x )}{x ^{\frac{3}{2}}} d x

Apply Integration By Parts

: - \frac{2 ln ( x )}{x} - \int - \frac{2}{x x} d x

= - \frac{2 ln ( x )}{x} - \int - \frac{2}{x x} d x

\int - \frac{2}{x x} d x = \frac{4}{x}

= - \frac{2 ln ( x )}{x} - \frac{4}{x}

Add a constant to the solution

= - \frac{2 ln ( x )}{x} - \frac{4}{x} + C

\frac{d}{d x} (\frac{10}{( x - 2 ) ^{3}})

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

\frac{\partial}{\partial x} (6 x + 2 y)

\frac{d}{d z} (\frac{z e ^{i z}}{( z - 2 ) ( z + 1 )})

\int (2 x - 2) e^{- x} d x

What is the integral of ((ln(x))/(sqrt(x^3))) ?
The integral of ((ln(x))/(sqrt(x^3))) is -(2ln(x))/(sqrt(x))-4/(sqrt(x))+C