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Similar expressions
(1/3x+4x^3)

Integral of (1/3x-4x^3) dx

The solution

You have entered [src]

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

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

Integral(x/3 - 4*x^3, (x, -3, 4))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 x^{3}\right)\, dx = - 4 \int x^{3}\, dx$
  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:
  
  $\int \frac{x}{3}\, dx = \frac{\int x\, dx}{3}$
  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: $\frac{x^{2}}{6}$
The result is: $- x^{4} + \frac{x^{2}}{6}$
Add the constant of integration:

$- x^{4} + \frac{x^{2}}{6}+ \mathrm{constant}$

The answer is:

$- x^{4} + \frac{x^{2}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                           2
 | /x      3\           4   x 
 | |- - 4*x | dx = C - x  + --
 | \3       /               6 
 |                            
/

$$\int \left(- 4 x^{3} + \frac{x}{3}\right)\, dx = C - x^{4} + \frac{x^{2}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1043/6

$$- \frac{1043}{6}$$

-1043/6

$$- \frac{1043}{6}$$

-1043/6

Numerical answer [src]

-173.833333333333

-173.833333333333

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

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Integral of (1/3x-4x^3) dx

Limits of integration:

The graph:

Piecewise:

The solution