What is the integral of-(4x+10)/(x^3) ?

The integral of-(4x+10)/(x^3) is 4/x+5/(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-(4x+10)/(x^3)

\int - \frac{4 x + 10}{x ^{3}} d x

\frac{4}{x} + \frac{5}{x ^{2}} + C

Solution steps

\int - \frac{4 x + 10}{x ^{3}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{4 x + 10}{x ^{3}} d x

Expand

\frac{4 x + 10}{x ^{3}} : \frac{4}{x ^{2}} + \frac{10}{x ^{3}}

= - \int \frac{4}{x ^{2}} + \frac{10}{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 \frac{4}{x ^{2}} d x + \int \frac{10}{x ^{3}} d x)

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

\int \frac{10}{x ^{3}} d x = - \frac{5}{x ^{2}}

= - (- \frac{4}{x} - \frac{5}{x ^{2}})

Simplify

= \frac{4}{x} + \frac{5}{x ^{2}}

Add a constant to the solution

= \frac{4}{x} + \frac{5}{x ^{2}} + C

x \to 0 - lim (\frac{4}{tan ( x )})

\int e^{- s t} \cdot t d t

9 arcsec (x)

\frac{\partial}{\partial y} (x y (\frac{1}{y ^{3}} + 2))

\int \frac{1}{4} e^{4 x + 1} d x

What is the integral of-(4x+10)/(x^3) ?
The integral of-(4x+10)/(x^3) is 4/x+5/(x^2)+C