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Integral of d{x}:
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Integral of 4*x*exp(x^2)
Graphing y =:
x^4+4x^3
Identical expressions
x^ four +4x^ three
x to the power of 4 plus 4x cubed
x to the power of four plus 4x to the power of three
x4+4x3
x⁴+4x³
x to the power of 4+4x to the power of 3
x^4+4x^3dx
Similar expressions
x^4-4x^3

Integral of x^4+4x^3 dx

The solution

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  0               
  /               
 |                
 |  / 4      3\   
 |  \x  + 4*x / dx
 |                
/                 
0

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

Integral(x^4 + 4*x^3, (x, 0, 0))

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:
  
  $\int 4 x^{3}\, dx = 4 \int x^{3}\, dx$
  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: $x^{4}$
The result is: $\frac{x^{5}}{5} + x^{4}$
Now simplify:

$\frac{x^{4} \left(x + 5\right)}{5}$
Add the constant of integration:

$\frac{x^{4} \left(x + 5\right)}{5}+ \mathrm{constant}$

The answer is:

$\frac{x^{4} \left(x + 5\right)}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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+4x^3 dx

Limits of integration:

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Piecewise:

The solution