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Identical expressions
(two x- five)dx/x^2+ four
(2x minus 5)dx divide by x squared plus 4
(two x minus five)dx divide by x squared plus four
(2x-5)dx/x2+4
2x-5dx/x2+4
(2x-5)dx/x²+4
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2x-5dx/x^2+4
(2x-5)dx divide by x^2+4
Similar expressions
(2x+5)dx/x^2+4
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Integral of (2x-5)dx/x^2+4 dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |  /2*x - 5    \   
 |  |------- + 4| dx
 |  |    2      |   
 |  \   x       /   
 |                  
/                   
0

$$\int\limits_{0}^{1} \left(4 + \frac{2 x - 5}{x^{2}}\right)\, dx$$

Integral((2*x - 5)/x^2 + 4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
1. Rewrite the integrand:
  
  $\frac{2 x - 5}{x^{2}} = \frac{2}{x} - \frac{5}{x^{2}}$
2. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{2}{x}\, dx = 2 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $2 \log{\left(x \right)}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{5}{x^{2}}\right)\, dx = - 5 \int \frac{1}{x^{2}}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
    So, the result is: $\frac{5}{x}$
  The result is: $2 \log{\left(x \right)} + \frac{5}{x}$
The result is: $4 x + 2 \log{\left(x \right)} + \frac{5}{x}$
Add the constant of integration:

$4 x + 2 \log{\left(x \right)} + \frac{5}{x}+ \mathrm{constant}$

The answer is:

$4 x + 2 \log{\left(x \right)} + \frac{5}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 | /2*x - 5    \                           5
 | |------- + 4| dx = C + 2*log(x) + 4*x + -
 | |    2      |                           x
 | \   x       /                            
 |                                          
/

$$\int \left(4 + \frac{2 x - 5}{x^{2}}\right)\, dx = C + 4 x + 2 \log{\left(x \right)} + \frac{5}{x}$$

Simplify

The answer [src]

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$$-\infty$$

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$$-\infty$$

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Numerical answer [src]

-6.89661838974298e+19

-6.89661838974298e+19

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

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Integral of (2x-5)dx/x^2+4 dx

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The solution