What is the integral of (14x^3+2x+1)/(x^3) ?

The integral of (14x^3+2x+1)/(x^3) is 14x-2/x-1/(2x^2)+C

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integral of (14x^3+2x+1)/(x^3)

\int \frac{14 x ^{3} + 2 x + 1}{x ^{3}} d x

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

Solution steps

\int \frac{14 x ^{3} + 2 x + 1}{x ^{3}} d x

Expand

\frac{14 x ^{3} + 2 x + 1}{x ^{3}} : 14 + \frac{2}{x ^{2}} + \frac{1}{x ^{3}}

= \int 14 + \frac{2}{x ^{2}} + \frac{1}{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 14 d x + \int \frac{2}{x ^{2}} d x + \int \frac{1}{x ^{3}} d x

\int 14 d x = 14 x

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

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

= 14 x - \frac{2}{x} - \frac{1}{2 x ^{2}}

Add a constant to the solution

= 14 x - \frac{2}{x} - \frac{1}{2 x ^{2}} + C

What is the integral of (14x^3+2x+1)/(x^3) ?
The integral of (14x^3+2x+1)/(x^3) is 14x-2/x-1/(2x^2)+C