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

The integral of (x+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+1/(x^3))

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

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

Solution steps

\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

n = 1 \sum \infty \frac{1}{2} (0.3)^{n}

f (x) = \frac{3}{x}, at x = - 5

\frac{( s ^{2} )}{s ^{2} + 1}

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

\int_{\frac{1}{2}}^{3} 16 x ln (2 x) d x

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