What is the integral of (x/2-1/x+3/(x^3)-4/(x^4)) ?

The integral of (x/2-1/x+3/(x^3)-4/(x^4)) is (x^2)/4-ln|x|-3/(2x^2)+4/(3x^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x/2-1/x+3/(x^3)-4/(x^4))

\int (\frac{x}{2} - \frac{1}{x} + \frac{3}{x ^{3}} - \frac{4}{x ^{4}}) d x

\frac{x ^{2}}{4} - ln ∣ x ∣ - \frac{3}{2 x ^{2}} + \frac{4}{3 x ^{3}} + C

Solution steps

\int \frac{x}{2} - \frac{1}{x} + \frac{3}{x ^{3}} - \frac{4}{x ^{4}} 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{x}{2} d x - \int \frac{1}{x} d x + \int \frac{3}{x ^{3}} d x - \int \frac{4}{x ^{4}} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

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

= \frac{x ^{2}}{4} - ln ∣ x ∣ - \frac{3}{2 x ^{2}} - (- \frac{4}{3 x ^{3}})

Simplify

= \frac{x ^{2}}{4} - ln ∣ x ∣ - \frac{3}{2 x ^{2}} + \frac{4}{3 x ^{3}}

Add a constant to the solution

= \frac{x ^{2}}{4} - ln ∣ x ∣ - \frac{3}{2 x ^{2}} + \frac{4}{3 x ^{3}} + C

\int sec (t) (7 sec (t) + 4 tan (t)) d t

\int cos^{18} (θ) sin (θ) d θ

\int 3 r^{2} d r

\int 4 x e^{x + 2} d x

\int (5 x^{2}) e^{- x^{3}} d x

What is the integral of (x/2-1/x+3/(x^3)-4/(x^4)) ?
The integral of (x/2-1/x+3/(x^3)-4/(x^4)) is (x^2)/4-ln|x|-3/(2x^2)+4/(3x^3)+C