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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^4+1)/x

\int \frac{x ^{4} + 1}{x} d x

\frac{x ^{4}}{4} + ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{4} + 1}{x} d x

Expand

\frac{x ^{4} + 1}{x} : x^{3} + \frac{1}{x}

= \int x^{3} + \frac{1}{x} 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 x^{3} d x + \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{4}}{4} + ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{4}}{4} + ln ∣ x ∣ + C

\int x^{7} e^{2 x} d x

\int \frac{1}{x - b} d x

\int sin (2 x) d x

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

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

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