What is the integral of (x+1)/(sqrt(x^5)) ?

The integral of (x+1)/(sqrt(x^5)) is -2/(sqrt(x))-2/(3x^{3/2)}+C

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integral of (x+1)/(sqrt(x^5))

\int \frac{x + 1}{x ^{5}} d x

- \frac{2}{x} - \frac{2}{3 x ^{\frac{3}{2}}} + C

Solution steps

\int \frac{x + 1}{x ^{5}} d x

Expand

\frac{x + 1}{x ^{5}} : \frac{x}{x ^{5}} + \frac{1}{x ^{5}}

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 ^{5}} d x + \int \frac{1}{x ^{5}} d x

\int \frac{x}{x ^{5}} d x = - \frac{2}{x}

\int \frac{1}{x ^{5}} d x = - \frac{2}{3 x ^{\frac{3}{2}}}

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

Add a constant to the solution

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

x^{2} y^{^{''}} + 2 x y^{^{'}} - 20 y = 0

\int \frac{3}{e ^{x} + 2} d x

\frac{d}{d x} (3^{5 x})

\frac{d}{d x} (9 sec (x - \frac{π}{2}))

x^{10}

What is the integral of (x+1)/(sqrt(x^5)) ?
The integral of (x+1)/(sqrt(x^5)) is -2/(sqrt(x))-2/(3x^{3/2)}+C