What is the integral of ((x^7+3x^5-2x^3-4))/(x^3) ?

The integral of ((x^7+3x^5-2x^3-4))/(x^3) is (x^5)/5+x^3-2x+2/(x^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^7+3x^5-2x^3-4))/(x^3)

\int \frac{( x ^{7} + 3 x ^{5} - 2 x ^{3} - 4 )}{x ^{3}} d x

\frac{x ^{5}}{5} + x^{3} - 2 x + \frac{2}{x ^{2}} + C

Solution steps

\int \frac{x ^{7} + 3 x ^{5} - 2 x ^{3} - 4}{x ^{3}} d x

Expand

\frac{x ^{7} + 3 x ^{5} - 2 x ^{3} - 4}{x ^{3}} : x^{4} + 3 x^{2} - 2 - \frac{4}{x ^{3}}

= \int x^{4} + 3 x^{2} - 2 - \frac{4}{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^{4} d x + \int 3 x^{2} d x - \int 2 d x - \int \frac{4}{x ^{3}} d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 2 d x = 2 x

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

= \frac{x ^{5}}{5} + x^{3} - 2 x - (- \frac{2}{x ^{2}})

Simplify

= \frac{x ^{5}}{5} + x^{3} - 2 x + \frac{2}{x ^{2}}

Add a constant to the solution

= \frac{x ^{5}}{5} + x^{3} - 2 x + \frac{2}{x ^{2}} + C

\frac{\partial}{\partial y} (1000 - 4 x y + x y^{2})

\frac{\partial}{\partial x} (e^{- 3 t} cos (π x))

\int_{0}^{\frac{5}{7}} 5 x - 7 x^{2} d x

x \to 0 + lim (x^{8 x})

\frac{3}{x - 4}

What is the integral of ((x^7+3x^5-2x^3-4))/(x^3) ?
The integral of ((x^7+3x^5-2x^3-4))/(x^3) is (x^5)/5+x^3-2x+2/(x^2)+C