What is the integral of ((x+1)^3)/(x^3) ?

The integral of ((x+1)^3)/(x^3) is ((x+1)^3)/(x^2)+3(ln|x|-2/x-1/(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+1)^3)/(x^3)

integral

\frac{( x + 1 ) ^{3}}{x ^{3}}

\frac{( x + 1 ) ^{3}}{x ^{2}} + 3 (ln ∣ x ∣ - \frac{2}{x} - \frac{1}{2 x ^{2}}) + C

Solution steps

\int \frac{( x + 1 ) ^{3}}{x ^{3}} d x

Apply Integration By Parts

: \frac{( x + 1 ) ^{3}}{x ^{2}} - \int - \frac{3 ( x + 1 ) ^{2}}{x ^{3}} d x

= \frac{( x + 1 ) ^{3}}{x ^{2}} - \int - \frac{3 ( x + 1 ) ^{2}}{x ^{3}} d x

\int - \frac{3 ( x + 1 ) ^{2}}{x ^{3}} d x = - 3 (ln ∣ x ∣ - \frac{2}{x} - \frac{1}{2 x ^{2}})

= \frac{( x + 1 ) ^{3}}{x ^{2}} - (- 3 (ln ∣ x ∣ - \frac{2}{x} - \frac{1}{2 x ^{2}}))

Simplify

= \frac{( x + 1 ) ^{3}}{x ^{2}} + 3 (ln ∣ x ∣ - \frac{2}{x} - \frac{1}{2 x ^{2}})

Add a constant to the solution

= \frac{( x + 1 ) ^{3}}{x ^{2}} + 3 (ln ∣ x ∣ - \frac{2}{x} - \frac{1}{2 x ^{2}}) + C

cot^{4} (x) - cot^{2} (x)

\frac{6}{x ^{3}}

y = x^{2} + x - 12

\frac{x + 1}{( x ^{2} + 4 x + 8 )}

\frac{u}{( 1 + u )}

What is the integral of ((x+1)^3)/(x^3) ?
The integral of ((x+1)^3)/(x^3) is ((x+1)^3)/(x^2)+3(ln|x|-2/x-1/(2x^2))+C