Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2*e^(x*(-2))
Integral of e^(-x^3)
Integral of -exp(-3*x)
Integral of x/(x^3+8)
Derivative of:
5x^(-6)
Identical expressions
5x^(- six)
5x to the power of ( minus 6)
5x to the power of ( minus six)
5x(-6)
5x-6
5x^-6
5x^(-6)dx
Similar expressions
5x^(6)

Solving integrals/ 5x^(-6)

Integral of 5x^(-6) dx

The solution

You have entered [src]

$$\int\limits_{1}^{\infty} \frac{5}{x^{6}}\, dx$$

Integral(5/x^6, (x, 1, oo))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{5}{x^{6}}\, dx = 5 \int \frac{1}{x^{6}}\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \frac{1}{x^{6}}\, dx = - \frac{1}{5 x^{5}}$
So, the result is: $- \frac{1}{x^{5}}$
Add the constant of integration:

$- \frac{1}{x^{5}}+ \mathrm{constant}$

The answer is:

$- \frac{1}{x^{5}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /              
 |               
 | 5           1 
 | -- dx = C - --
 |  6           5
 | x           x 
 |               
/

$$\int \frac{5}{x^{6}}\, dx = C - \frac{1}{x^{5}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

=

$$1$$

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