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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1-2x^3)/(x^3)

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

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

Solution steps

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

Expand

\frac{1 - 2 x ^{3}}{x ^{3}} : \frac{1}{x ^{3}} - 2

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int (3 + x^{4}) (8 + x^{3}) d x

\int sec (x) (3 sec (x) + 5 tan (x)) d x

\int \frac{1}{2 a x} d x

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

\int x^{17} d x

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