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

Popular >

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

\int_{2}^{5} \frac{x}{x ^{2} + 6 x + 13} d x

\frac{\partial}{\partial x} (5 y^{6} cos (5 x))

f (x) = \frac{6 - x ^{2}}{6 + x ^{2}}

\frac{d ^{3}}{d x ^{3}} (ln (1 + x))

k = 1 \sum \infty \frac{k}{e ^{7 k}}

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