What is the integral of (x^4+9)/(x^3) ?

The integral of (x^4+9)/(x^3) is (x^2)/2-9/(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 (x^4+9)/(x^3)

\int \frac{x ^{4} + 9}{x ^{3}} d x

\frac{x ^{2}}{2} - \frac{9}{2 x ^{2}} + C

Solution steps

\int \frac{x ^{4} + 9}{x ^{3}} d x

Expand

\frac{x ^{4} + 9}{x ^{3}} : x + \frac{9}{x ^{3}}

= \int x + \frac{9}{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 x d x + \int \frac{9}{x ^{3}} d x

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

\int \frac{9}{x ^{3}} d x = - \frac{9}{2 x ^{2}}

= \frac{x ^{2}}{2} - \frac{9}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{9}{2 x ^{2}} + C

x y^{^{'}} = - 3 y

\int arctan (\frac{x}{3}) d x

\int x^{9} x^{5} + 6 d x

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

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

What is the integral of (x^4+9)/(x^3) ?
The integral of (x^4+9)/(x^3) is (x^2)/2-9/(2x^2)+C