Integral of x^-3 dx

You have entered [src]

$$\int\limits_{0}^{1} \frac{1}{x^{3}}\, dx$$

Integral(x^(-3), (x, 0, 1))

Detail solution

The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :

$\int \frac{1}{x^{3}}\, dx = - \frac{1}{2 x^{2}}$
Add the constant of integration:

$- \frac{1}{2 x^{2}}+ \mathrm{constant}$

The answer is:

$- \frac{1}{2 x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                
 |                 
 | 1            1  
 | -- dx = C - ----
 |  3             2
 | x           2*x 
 |                 
/

$$\int \frac{1}{x^{3}}\, dx = C - \frac{1}{2 x^{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

9.15365037903492e+37

9.15365037903492e+37

The graph

Use the examples entering the upper and lower limits of integration.