What is the integral of (-4x-10)/(x^3) ?

The integral of (-4x-10)/(x^3) is (2x+5)/(x^2)+2/x+C

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integral of (-4x-10)/(x^3)

\int \frac{- 4 x - 10}{x ^{3}} d x

\frac{2 x + 5}{x ^{2}} + \frac{2}{x} + C

Solution steps

\int \frac{- 4 x - 10}{x ^{3}} d x

Apply Integration By Parts

: \frac{2 x + 5}{x ^{2}} - \int \frac{2}{x ^{2}} d x

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

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

= \frac{2 x + 5}{x ^{2}} - (- \frac{2}{x})

Simplify

= \frac{2 x + 5}{x ^{2}} + \frac{2}{x}

Add a constant to the solution

= \frac{2 x + 5}{x ^{2}} + \frac{2}{x} + C

f (x) = x^{2} - 12, g (x) = x - 6, x = - 2, x = 3

\int 3 x^{7} + 4 x^{5} - 2 x^{3} - x + 1 d x

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

\frac{\partial}{\partial x} (z e^{x y})

\frac{d}{d x} (\frac{1400}{( 1 + 6 e ^{- 0.02 x} )})

What is the integral of (-4x-10)/(x^3) ?
The integral of (-4x-10)/(x^3) is (2x+5)/(x^2)+2/x+C