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Derivative of:
5x^4+2x^3
Equation:
5x^4+2x^3
Identical expressions
5x^ four +2x^ three
5x to the power of 4 plus 2x cubed
5x to the power of four plus 2x to the power of three
5x4+2x3
5x⁴+2x³
5x to the power of 4+2x to the power of 3
5x^4+2x^3dx
Similar expressions
5x^4-2x^3

Solving integrals/ 5x^4+2x^3

Integral of 5x^4+2x^3 dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |  /   4      3\   
 |  \5*x  + 2*x / dx
 |                  
/                   
0

$$\int\limits_{0}^{1} \left(5 x^{4} + 2 x^{3}\right)\, dx$$

Integral(5*x^4 + 2*x^3, (x, 0, 1))

Detail solution

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

$x^{4} \left(x + \frac{1}{2}\right)$
Add the constant of integration:

$x^{4} \left(x + \frac{1}{2}\right)+ \mathrm{constant}$

The answer is:

$x^{4} \left(x + \frac{1}{2}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(5 x^{4} + 2 x^{3}\right)\, dx = C + x^{5} + \frac{x^{4}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/2

$$\frac{3}{2}$$

3/2

$$\frac{3}{2}$$

3/2

Numerical answer [src]

1.5

1.5

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 5x^4+2x^3 dx

Limits of integration:

The graph:

Piecewise:

The solution