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Identical expressions
5x⁴-8x³+9x³+ seven
5x⁴ minus 8x³ plus 9x³ plus 7
5x⁴ minus 8x³ plus 9x³ plus seven
5x⁴-8x³+9x³+7dx
Similar expressions
5x⁴-8x³-9x³+7
5x⁴-8x³+9x³-7
5x⁴+8x³+9x³+7

Integral of 5x⁴-8x³+9x³+7 dx

The solution

You have entered [src]

  4                            
  /                            
 |                             
 |  /   4      3      3    \   
 |  \5*x  - 8*x  + 9*x  + 7/ dx
 |                             
/                              
1

$$\int\limits_{1}^{4} \left(\left(9 x^{3} + \left(5 x^{4} - 8 x^{3}\right)\right) + 7\right)\, dx$$

Integral(5*x^4 - 8*x^3 + 9*x^3 + 7, (x, 1, 4))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 9 x^{3}\, dx = 9 \int x^{3}\, dx$
    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: $\frac{9 x^{4}}{4}$
  1. Integrate term-by-term:
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int 5 x^{4}\, dx = 5 \int x^{4}\, dx$
      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:
      
      $\int \left(- 8 x^{3}\right)\, dx = - 8 \int x^{3}\, dx$
      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: $- 2 x^{4}$
    The result is: $x^{5} - 2 x^{4}$
  The result is: $x^{5} + \frac{x^{4}}{4}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 7\, dx = 7 x$
The result is: $x^{5} + \frac{x^{4}}{4} + 7 x$
Now simplify:

$x \left(x^{4} + \frac{x^{3}}{4} + 7\right)$
Add the constant of integration:

$x \left(x^{4} + \frac{x^{3}}{4} + 7\right)+ \mathrm{constant}$

The answer is:

$x \left(x^{4} + \frac{x^{3}}{4} + 7\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                               4
 | /   4      3      3    \           5         x 
 | \5*x  - 8*x  + 9*x  + 7/ dx = C + x  + 7*x + --
 |                                              4 
/

$$\int \left(\left(9 x^{3} + \left(5 x^{4} - 8 x^{3}\right)\right) + 7\right)\, dx = C + x^{5} + \frac{x^{4}}{4} + 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

4431/4

$$\frac{4431}{4}$$

4431/4

$$\frac{4431}{4}$$

4431/4

Numerical answer [src]

1107.75

1107.75

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

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Integral of 5x⁴-8x³+9x³+7 dx

Limits of integration:

The graph:

Piecewise:

The solution