What is the integral of 1/(sqrt(2x^3)) ?

The integral of 1/(sqrt(2x^3)) is -sqrt(2/x)+C

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integral of 1/(sqrt(2x^3))

\int \frac{1}{2 x ^{3}} d x

- \frac{2}{x} + C

Solution steps

\int \frac{1}{2 x ^{3}} d x

Apply Integration By Parts

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

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

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

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

Simplify

\frac{x}{2 x ^{2}} - \frac{3}{2 x} : - \frac{2}{x}

= - \frac{2}{x}

Add a constant to the solution

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

f (x) = 3 - (- 27)

y^{^{''}} + 16 y = t sin (4 t)

f (x) = (2 x^{2} - 1)^{2} (3 x^{2})

e^{2 x}

2 sin (θ)

What is the integral of 1/(sqrt(2x^3)) ?
The integral of 1/(sqrt(2x^3)) is -sqrt(2/x)+C