What is integral of (5f(x))/(x^2(x+1)^3) ?

The answer to integral of (5f(x))/(x^2(x+1)^3) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5f(x))/(x^2(x+1)^3)

\int \frac{5 f ( x )}{x ^{2} ( x + 1 ) ^{3}} d x

\frac{5 f ( 2 x ^{2} ln ∣ x ∣ - 2 x ^{2} ln ∣ x + 1 ∣ + 2 x + 4 x ln ∣ x ∣ - 4 x ln ∣ x + 1 ∣ + 2 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + 3 )}{2 ( x + 1 ) ^{2}} + C

Solution steps

\int \frac{5 f x}{x ^{2} ( x + 1 ) ^{3}} d x

\int \frac{5 f x}{x ^{2} ( x + 1 ) ^{3}} d x = 5 f (ln ∣ x ∣ - ln ∣ x + 1 ∣ + \frac{1}{x + 1} + \frac{1}{2 ( x + 1 ) ^{2}}) + C

= 5 f (ln ∣ x ∣ - ln ∣ x + 1 ∣ + \frac{1}{x + 1} + \frac{1}{2 ( x + 1 ) ^{2}}) + C

Simplify

5 f (ln ∣ x ∣ - ln ∣ x + 1 ∣ + \frac{1}{x + 1} + \frac{1}{2 ( x + 1 ) ^{2}}) + C : \frac{5 f ( 2 x ^{2} ln ∣ x ∣ - 2 x ^{2} ln ∣ x + 1 ∣ + 2 x + 4 x ln ∣ x ∣ - 4 x ln ∣ x + 1 ∣ + 2 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + 3 )}{2 ( x + 1 ) ^{2}} + C

= \frac{5 f ( 2 x ^{2} ln ∣ x ∣ - 2 x ^{2} ln ∣ x + 1 ∣ + 2 x + 4 x ln ∣ x ∣ - 4 x ln ∣ x + 1 ∣ + 2 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + 3 )}{2 ( x + 1 ) ^{2}} + C

\int_{0}^{π} sin (n x) d x

\frac{- cos ( x )}{4 x ^{2} + 2 x - 3}

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

\frac{d y}{d t} = 4 y

n = 1 \sum \infty \frac{n + 1}{2 n + 1}

What is integral of (5f(x))/(x^2(x+1)^3) ?
The answer to integral of (5f(x))/(x^2(x+1)^3) is