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

The integral of x^3-1/(x^2)-x^{2/3} is (x^4)/4+1/x-3/5 x^{5/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{x ^{4}}{4} + \frac{1}{x} - \frac{3}{5} x^{\frac{5}{3}} + C

Solution steps

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

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

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

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

= \frac{x ^{4}}{4} - (- \frac{1}{x}) - \frac{3}{5} x^{\frac{5}{3}}

Simplify

= \frac{x ^{4}}{4} + \frac{1}{x} - \frac{3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{1}{x} - \frac{3}{5} x^{\frac{5}{3}} + C

What is the integral of x^3-1/(x^2)-x^{2/3} ?
The integral of x^3-1/(x^2)-x^{2/3} is (x^4)/4+1/x-3/5 x^{5/3}+C