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Integral of d{x}:
Integral of x/e^x
Integral of 1/e^x
Integral of e^(-3x)
Integral of x/x^2
Sum of series:
x/x^2
Canonical form:
x/x^2
Identical expressions
x/x^ two
x divide by x squared
x divide by x to the power of two
x/x2
x/x²
x/x to the power of 2
x divide by x^2
x/x^2dx
Similar expressions
ln^2(x)/x^2
dx/(x^2)(3rootx)
lnx/(x^2)
(1/e^x)/x^2
x/(x^2+2x+2)^2

Integral of x/x^2 dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{x}{x^{2}}\, dx$$

Integral(x/(x^2), (x, 0, 1))

Detail solution

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

$\int \frac{1}{x}\, dx = \frac{\int \frac{2}{x}\, dx}{2}$
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{1}{2 u}\, du$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\log{\left(u \right)}$
  Now substitute $u$ back in:
  
  $\log{\left(x^{2} \right)}$
So, the result is: $\frac{\log{\left(x^{2} \right)}}{2}$
Add the constant of integration:

$\frac{\log{\left(x^{2} \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(x^{2} \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   
 |                / 2\
 | x           log\x /
 | -- dx = C + -------
 |  2             2   
 | x                  
 |                    
/

$$\int \frac{x}{x^{2}}\, dx = C + \frac{\log{\left(x^{2} \right)}}{2}$$

Simplify

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

Упростить

Numerical answer [src]

44.0904461339929

44.0904461339929

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

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Integral of x/x^2 dx

Limits of integration:

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Piecewise:

The solution