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}}

Add a constant to the solution

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

\int \frac{2 e ^{2 x}}{1 + e ^{4 x}} d x

\frac{d y}{d x} = 5 - 8 x

\int \frac{a ^{x}}{b ^{x}} d x

\frac{- x ^{2} - 9}{( x ^{2} - 9 ) ^{2}}

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