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Similar expressions
(1-x)/x^2

Integral of (1+x)/x^2 dx

The solution

You have entered [src]

  1         
  /         
 |          
 |  1 + x   
 |  ----- dx
 |     2    
 |    x     
 |          
/           
0

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

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

Detail solution

Rewrite the integrand:

$\frac{x + 1}{x^{2}} = \frac{1}{x} + \frac{1}{x^{2}}$
Integrate term-by-term:
1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
The result is: $\log{\left(x \right)} - \frac{1}{x}$
Add the constant of integration:

$\log{\left(x \right)} - \frac{1}{x}+ \mathrm{constant}$

The answer is:

$\log{\left(x \right)} - \frac{1}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                          
 | 1 + x          1         
 | ----- dx = C - - + log(x)
 |    2           x         
 |   x                      
 |                          
/

$$\int \frac{x + 1}{x^{2}}\, dx = C + \log{\left(x \right)} - \frac{1}{x}$$

Simplify

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

1.3793236779486e+19

1.3793236779486e+19

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

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Integral of (1+x)/x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution