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

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

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

\int \frac{( x - 1 )}{x ^{5}} d x

- \frac{2 x - 1}{3 x ^{\frac{3}{2}}} + \frac{2}{3} \frac{x - 1}{x} + C

Solution steps

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

Simplify

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

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

Apply Integration By Parts

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

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

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

= - \frac{2 x - 1}{3 x ^{\frac{3}{2}}} - (- \frac{2}{3} \frac{x - 1}{x})

Simplify

= - \frac{2 x - 1}{3 x ^{\frac{3}{2}}} + \frac{2}{3} \frac{x - 1}{x}

Add a constant to the solution

= - \frac{2 x - 1}{3 x ^{\frac{3}{2}}} + \frac{2}{3} \frac{x - 1}{x} + C

\frac{\partial}{\partial z} (sin (z))

4 - x^{2}, x^{2} - 4

\frac{x ^{7} + 4}{x ^{7}}

y = 10 cos (x), (\frac{π}{3}, 5)

\frac{d y}{d x} = \frac{( 5 x sec ( \frac{y}{x} ) + y )}{x}

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