You entered:

(2x-5)÷x^2-5x+6dx

What you mean?

(2*x - 1*5)/(x^2 - 5*x + 6*dx)

(2*x - 1*5)*dx/(x^2 - 5*x + 6)

(2*x - 1*5)/(x^2 - 5*x) + 6*dx

(2*x - 1*5)*x/(x^2 - 1*5) + 6*dx

(2*x - 1*5)/(x^2) - 5*x + 6*dx

(2*x - 1*5)*2/x - 5*x + 6*dx

2*x - 5/(x^2) - 5*x + 6*dx

Integral of (2x-5)÷x^2-5x+6dx dx

The solution

You have entered [src]

  1                         
  /                         
 |                          
 |  /2*x - 5            \   
 |  |------- - 5*x + 6*1| dx
 |  |    2              |   
 |  \   x               /   
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(- 5 x + 6 \cdot 1 + \frac{2 x - 5}{x^{2}}\right)\, dx$$

Integral((2*x - 1*5)/(x^2) - 5*x + 6*1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 5 x\right)\, dx = - \int 5 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $\frac{5 x^{2}}{2}$
  So, the result is: $- \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 6 \cdot 1\, dx = 6 x$
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: $- \frac{5 x^{2}}{2} + 6 x + 2 \log{\left(x \right)} + \frac{5}{x}$
Add the constant of integration:

$- \frac{5 x^{2}}{2} + 6 x + 2 \log{\left(x \right)} + \frac{5}{x}+ \mathrm{constant}$

The answer is:

$- \frac{5 x^{2}}{2} + 6 x + 2 \log{\left(x \right)} + \frac{5}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                        
 |                                                        2
 | /2*x - 5            \                     5         5*x 
 | |------- - 5*x + 6*1| dx = C + 2*log(x) + - + 6*x - ----
 | |    2              |                     x          2  
 | \   x               /                                   
 |                                                         
/

$$2\,\log x-{{5\,x^2}\over{2}}+6\,x+{{5}\over{x}}$$

Simplify

The answer [src]

-oo

$${\it \%a}$$

-oo

$$-\infty$$

Упростить

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)÷x^2-5x+6dx dx

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