What is the integral of (5x+4)/(x^3) ?

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

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integral of (5x+4)/(x^3)

\int \frac{5 x + 4}{x ^{3}} d x

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

Solution steps

\int \frac{5 x + 4}{x ^{3}} d x

Expand

\frac{5 x + 4}{x ^{3}} : \frac{5}{x ^{2}} + \frac{4}{x ^{3}}

= \int \frac{5}{x ^{2}} + \frac{4}{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{5}{x ^{2}} d x + \int \frac{4}{x ^{3}} d x

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

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

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

Add a constant to the solution

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

\int e^{x^{3} - 3 x^{2}} d y

x \to 5 lim (\frac{6 x}{x - 5})

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

\frac{d}{d x} (\frac{1 + cos ( 2 x )}{1 - cos ( 2 x )})

\int x sin (\frac{1}{7} x) d x

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