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Integral of d{x}:
Integral of x^4-3x
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Identical expressions
x^ four -3x
x to the power of 4 minus 3x
x to the power of four minus 3x
x4-3x
x⁴-3x
x^4-3xdx
Similar expressions
x^4+3x
25x^(4)-3x^(2)-8

Solving integrals/ x^4-3x

Integral of x^4-3x dx

The solution

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  1              
  /              
 |               
 |  / 4      \   
 |  \x  - 3*x/ dx
 |               
/                
0

$$\int\limits_{0}^{1} \left(x^{4} - 3 x\right)\, dx$$

Integral(x^4 - 3*x, (x, 0, 1))

Detail solution

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

$\frac{x^{2} \cdot \left(2 x^{3} - 15\right)}{10}$
Add the constant of integration:

$\frac{x^{2} \cdot \left(2 x^{3} - 15\right)}{10}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \cdot \left(2 x^{3} - 15\right)}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                        2    5
 | / 4      \          3*x    x 
 | \x  - 3*x/ dx = C - ---- + --
 |                      2     5 
/

$${{x^5}\over{5}}-{{3\,x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-13 
----
 10

$$-{{13}\over{10}}$$

-13 
----
 10

$$- \frac{13}{10}$$

Simplify

Numerical answer [src]

-1.3

-1.3

The graph

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

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Identical expressions

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Integral of x^4-3x dx

Limits of integration:

The graph:

Piecewise:

The solution