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Integral of (5x^3-4x^2+7x^4)dx
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Identical expressions
(5x^ three - four x^ two +7x^4)dx
(5x cubed minus 4x squared plus 7x to the power of 4)dx
(5x to the power of three minus four x to the power of two plus 7x to the power of 4)dx
(5x3-4x2+7x4)dx
5x3-4x2+7x4dx
(5x³-4x²+7x⁴)dx
(5x to the power of 3-4x to the power of 2+7x to the power of 4)dx
5x^3-4x^2+7x^4dx
Similar expressions
(5x^3+4x^2+7x^4)dx
(5x^3-4x^2-7x^4)dx

Solving integrals/ (5x^3-4x^2+7x^4)dx

Integral of (5x^3-4x^2+7x^4)dx dx

The solution

You have entered [src]

  1                        
  /                        
 |                         
 |  /   3      2      4\   
 |  \5*x  - 4*x  + 7*x / dx
 |                         
/                          
0

$$\int\limits_{0}^{1} \left(7 x^{4} + \left(5 x^{3} - 4 x^{2}\right)\right)\, dx$$

Integral(5*x^3 - 4*x^2 + 7*x^4, (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:
  
  $\int 7 x^{4}\, dx = 7 \int x^{4}\, dx$
  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: $\frac{7 x^{5}}{5}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 5 x^{3}\, dx = 5 \int x^{3}\, dx$
    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: $\frac{5 x^{4}}{4}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 4 x^{2}\right)\, dx = - 4 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $- \frac{4 x^{3}}{3}$
  The result is: $\frac{5 x^{4}}{4} - \frac{4 x^{3}}{3}$
The result is: $\frac{7 x^{5}}{5} + \frac{5 x^{4}}{4} - \frac{4 x^{3}}{3}$
Now simplify:

$\frac{x^{3} \left(84 x^{2} + 75 x - 80\right)}{60}$
Add the constant of integration:

$\frac{x^{3} \left(84 x^{2} + 75 x - 80\right)}{60}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(84 x^{2} + 75 x - 80\right)}{60}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                  3      4      5
 | /   3      2      4\          4*x    5*x    7*x 
 | \5*x  - 4*x  + 7*x / dx = C - ---- + ---- + ----
 |                                3      4      5  
/

$$\int \left(7 x^{4} + \left(5 x^{3} - 4 x^{2}\right)\right)\, dx = C + \frac{7 x^{5}}{5} + \frac{5 x^{4}}{4} - \frac{4 x^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

79
--
60

$$\frac{79}{60}$$

79
--
60

$$\frac{79}{60}$$

79/60

Numerical answer [src]

1.31666666666667

1.31666666666667

The graph

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

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Integral of (5x^3-4x^2+7x^4)dx dx

Limits of integration:

The graph:

Piecewise:

The solution