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

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

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

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

\frac{4}{x} - \frac{5}{x ^{2}} + C

Solution steps

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

Expand

\frac{- 4 x + 10}{x ^{3}} : - \frac{4}{x ^{2}} + \frac{10}{x ^{3}}

= \int - \frac{4}{x ^{2}} + \frac{10}{x ^{3}} d x

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{4}{x ^{2}} d x + \int \frac{10}{x ^{3}} d x

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

\int \frac{10}{x ^{3}} d x = - \frac{5}{x ^{2}}

= - (- \frac{4}{x}) - \frac{5}{x ^{2}}

Simplify

= \frac{4}{x} - \frac{5}{x ^{2}}

Add a constant to the solution

= \frac{4}{x} - \frac{5}{x ^{2}} + C

{0}

\int (2 x + 5 y)^{6} d y

\int_{0}^{1} 2 π (x + 5) x^{2} d x

x \to 4 lim (8 - 3 x)

e^{2} x \frac{d y}{d x} - e^{x} y = e^{(- x)} y^{2}

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