What is the integral of ((3+2y)^2)/(y^5) ?

The integral of ((3+2y)^2)/(y^5) is -9/(4y^4)-4/(y^3)-2/(y^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((3+2y)^2)/(y^5)

\int \frac{( 3 + 2 y ) ^{2}}{y ^{5}} d y

- \frac{9}{4 y ^{4}} - \frac{4}{y ^{3}} - \frac{2}{y ^{2}} + C

Solution steps

\int \frac{( 3 + 2 y ) ^{2}}{y ^{5}} d y

Expand

\frac{( 3 + 2 y ) ^{2}}{y ^{5}} : \frac{9}{y ^{5}} + \frac{12}{y ^{4}} + \frac{4}{y ^{3}}

= \int \frac{9}{y ^{5}} + \frac{12}{y ^{4}} + \frac{4}{y ^{3}} d y

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{9}{y ^{5}} d y + \int \frac{12}{y ^{4}} d y + \int \frac{4}{y ^{3}} d y

\int \frac{9}{y ^{5}} d y = - \frac{9}{4 y ^{4}}

\int \frac{12}{y ^{4}} d y = - \frac{4}{y ^{3}}

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

= - \frac{9}{4 y ^{4}} - \frac{4}{y ^{3}} - \frac{2}{y ^{2}}

Add a constant to the solution

= - \frac{9}{4 y ^{4}} - \frac{4}{y ^{3}} - \frac{2}{y ^{2}} + C

\int 2 x y^{3} + y^{6} d x

\int \frac{x ^{2}}{x ^{3} + 10} d x

\int \frac{2}{5} - \frac{1}{25} x d x

\int sin (x) - 3 cos (x) d x

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

What is the integral of ((3+2y)^2)/(y^5) ?
The integral of ((3+2y)^2)/(y^5) is -9/(4y^4)-4/(y^3)-2/(y^2)+C