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Identical expressions
(4x^ three -3x^ two + two ^x+ one)
(4x cubed minus 3x squared plus 2 to the power of x plus 1)
(4x to the power of three minus 3x to the power of two plus two to the power of x plus one)
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4x3-3x2+2x+1
(4x³-3x²+2^x+1)
(4x to the power of 3-3x to the power of 2+2 to the power of x+1)
4x^3-3x^2+2^x+1
(4x^3-3x^2+2^x+1)dx
Similar expressions
(4x^3+3x^2+2^x+1)
(4x^3-3x^2+2^x-1)
(4x^3-3x^2-2^x+1)

Solving integrals/ (4x^3-3x^2+2^x+1)

Integral of (4x^3-3x^2+2^x+1) dx

The solution

You have entered [src]

  3                          
  /                          
 |                           
 |  /   3      2    x    \   
 |  \4*x  - 3*x  + 2  + 1/ dx
 |                           
/                            
-2

$$\int\limits_{-2}^{3} \left(2^{x} + 4 x^{3} - 3 x^{2} + 1\right)\, dx$$

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

Detail solution

Integrate term-by-term:
1. The integral of an exponential function is itself divided by the natural logarithm of the base.
  
  $\int 2^{x}\, dx = \frac{2^{x}}{\log{\left(2 \right)}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x^{3}\, dx = 4 \int x^{3}\, dx$
  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: $x^{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 x^{2}\right)\, dx = - \int 3 x^{2}\, dx$
  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: $x^{3}$
  So, the result is: $- x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{2^{x}}{\log{\left(2 \right)}} + x^{4} - x^{3} + x$
Add the constant of integration:

$\frac{2^{x}}{\log{\left(2 \right)}} + x^{4} - x^{3} + x+ \mathrm{constant}$

The answer is:

$\frac{2^{x}}{\log{\left(2 \right)}} + x^{4} - x^{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                    
 |                                                  x  
 | /   3      2    x    \               4    3     2   
 | \4*x  - 3*x  + 2  + 1/ dx = C + x + x  - x  + ------
 |                                               log(2)
/

$$\int \left(2^{x} + 4 x^{3} - 3 x^{2} + 1\right)\, dx = \frac{2^{x}}{\log{\left(2 \right)}} + C + x^{4} - x^{3} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

        31   
35 + --------
     4*log(2)

$$\frac{31}{4 \log{\left(2 \right)}} + 35$$

        31   
35 + --------
     4*log(2)

$$\frac{31}{4 \log{\left(2 \right)}} + 35$$

Упростить

Numerical answer [src]

46.1808865668895

46.1808865668895

The graph

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

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Integral of (4x^3-3x^2+2^x+1) dx

Limits of integration:

The graph:

Piecewise:

The solution