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Identical expressions
(x^ six - three x^3+ five)
(x to the power of 6 minus 3x cubed plus 5)
(x to the power of six minus three x cubed plus five)
(x6-3x3+5)
x6-3x3+5
(x⁶-3x³+5)
(x to the power of 6-3x to the power of 3+5)
x^6-3x^3+5
(x^6-3x^3+5)dx
Similar expressions
(x^6+3x^3+5)
(x^6-3x^3-5)

Integral of (x^6-3x^3+5) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  / 6      3    \   
 |  \x  - 3*x  + 5/ dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(x^{6} - 3 x^{3}\right) + 5\right)\, dx$$

Integral(x^6 - 3*x^3 + 5, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{6}\, dx = \frac{x^{7}}{7}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 3 x^{3}\right)\, dx = - 3 \int x^{3}\, dx$
    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: $- \frac{3 x^{4}}{4}$
  The result is: $\frac{x^{7}}{7} - \frac{3 x^{4}}{4}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $\frac{x^{7}}{7} - \frac{3 x^{4}}{4} + 5 x$
Now simplify:

$\frac{x \left(4 x^{6} - 21 x^{3} + 140\right)}{28}$
Add the constant of integration:

$\frac{x \left(4 x^{6} - 21 x^{3} + 140\right)}{28}+ \mathrm{constant}$

The answer is:

$\frac{x \left(4 x^{6} - 21 x^{3} + 140\right)}{28}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                        
 |                                   4    7
 | / 6      3    \                3*x    x 
 | \x  - 3*x  + 5/ dx = C + 5*x - ---- + --
 |                                 4     7 
/

$$\int \left(\left(x^{6} - 3 x^{3}\right) + 5\right)\, dx = C + \frac{x^{7}}{7} - \frac{3 x^{4}}{4} + 5 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

123
---
 28

$$\frac{123}{28}$$

123
---
 28

$$\frac{123}{28}$$

123/28

Numerical answer [src]

4.39285714285714

4.39285714285714

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

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Integral of (x^6-3x^3+5) dx

Limits of integration:

The graph:

Piecewise:

The solution