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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{d}{d x} (sin (x^{2} - 2 x + 6))

y^{2} = x + 1, x = 1

\int sin^{10} (x) d x

f (x) = \frac{4}{x ^{2}}, (1, 4)

f (x) = (3 - e^{- 4 x})^{4}

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