What is the integral of ((7x^9-20x^6))/(x^3) ?

The integral of ((7x^9-20x^6))/(x^3) is x^7-5x^4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((7x^9-20x^6))/(x^3)

\int \frac{( 7 x ^{9} - 20 x ^{6} )}{x ^{3}} d x

x^{7} - 5 x^{4} + C

Solution steps

\int \frac{7 x ^{9} - 20 x ^{6}}{x ^{3}} d x

Expand

\frac{7 x ^{9} - 20 x ^{6}}{x ^{3}} : \frac{7 x ^{9}}{x ^{3}} - \frac{20 x ^{6}}{x ^{3}}

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{7 x ^{9}}{x ^{3}} d x - \int \frac{20 x ^{6}}{x ^{3}} d x

\int \frac{7 x ^{9}}{x ^{3}} d x = x^{7}

\int \frac{20 x ^{6}}{x ^{3}} d x = 5 x^{4}

= x^{7} - 5 x^{4}

Add a constant to the solution

= x^{7} - 5 x^{4} + C

\int (tan (x) + \frac{1}{tan ( x )})^{2} d x

x^{2} y^{^{''}} - 2 y = sin (ln (x))

x \to - 2 lim (2 x)

\int \frac{1}{5 x ^{7}} d x

\frac{arctan ( x )}{x + 1}

What is the integral of ((7x^9-20x^6))/(x^3) ?
The integral of ((7x^9-20x^6))/(x^3) is x^7-5x^4+C