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Similar expressions
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Integral of 3x^3-2x+1dx/x^2 dx

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |  /   3         1 \   
 |  |3*x  - 2*x + --| dx
 |  |              2|   
 |  \             x /   
 |                      
/                       
0

$$\int\limits_{0}^{1} \left(\left(3 x^{3} - 2 x\right) + \frac{1}{x^{2}}\right)\, dx$$

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

Detail solution

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

$\text{NaN}+ \mathrm{constant}$

The answer is:

$\text{NaN}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                           
 | /   3         1 \         
 | |3*x  - 2*x + --| dx = nan
 | |              2|         
 | \             x /         
 |                           
/

$$\int \left(\left(3 x^{3} - 2 x\right) + \frac{1}{x^{2}}\right)\, dx = \text{NaN}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

1.3793236779486e+19

1.3793236779486e+19

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

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Identical expressions

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Integral of 3x^3-2x+1dx/x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution