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

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

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

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

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

Solution steps

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

Expand

\frac{x + 1}{x ^{3}} : \frac{x}{x ^{3}} + \frac{1}{x ^{3}}

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{x}{x ^{3}} d x + \int \frac{1}{x ^{3}} d x

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

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

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

Add a constant to the solution

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

z \to i lim (z^{2} + 2 z)

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{e ^{2 x}}{x}

\frac{d}{d x} (\frac{4 x}{x ^{2} + 1})

\frac{d}{d s} (\frac{s}{s ^{2} + 25})

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