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(three x^3+4x^ two - five)/(x)
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3x^3+4x^2-5/x
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Similar expressions
(3x^3+4x^2+5)/(x)
(3x^3-4x^2-5)/(x)

Integral of (3x^3+4x^2-5)/(x) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |     3      2       
 |  3*x  + 4*x  - 5   
 |  --------------- dx
 |         x          
 |                    
/                     
0

$$\int\limits_{0}^{1} \frac{3 x^{3} + 4 x^{2} - 5}{x}\, dx$$

Integral((3*x^3 + 4*x^2 - 1*5)/x, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{3 x^{3} + 4 x^{2} - 5}{x} = 3 x^{2} + 4 x - \frac{5}{x}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $x^{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x\, dx = 4 \int x\, dx$
  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: $2 x^{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{5}{x}\right)\, dx = - 5 \int \frac{1}{x}\, dx$
  1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  So, the result is: $- 5 \log{\left(x \right)}$
The result is: $x^{3} + 2 x^{2} - 5 \log{\left(x \right)}$
Add the constant of integration:

$x^{3} + 2 x^{2} - 5 \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$x^{3} + 2 x^{2} - 5 \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                             
 |                                              
 |    3      2                                  
 | 3*x  + 4*x  - 5           3                 2
 | --------------- dx = C + x  - 5*log(x) + 2*x 
 |        x                                     
 |                                              
/

$$\int \frac{3 x^{3} + 4 x^{2} - 5}{x}\, dx = C + x^{3} + 2 x^{2} - 5 \log{\left(x \right)}$$

Simplify

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

Упростить

Numerical answer [src]

-217.452230669964

-217.452230669964

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

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Integral of (3x^3+4x^2-5)/(x) dx

Limits of integration:

The graph:

Piecewise:

The solution