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

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

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

\frac{x ^{2}}{2} - \frac{1}{2 x ^{2}} + C

Solution steps

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

Expand

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

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

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

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

= \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}} + C

\int (2 x + 10)^{20} d x

\int sin (arctan (x)) d x

\int \frac{7}{( x - 9 ) ( x - 2 )} d x

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

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