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Identical expressions
(7x²+3x³+4x^ five)
(7x² plus 3x³ plus 4x to the power of 5)
(7x² plus 3x³ plus 4x to the power of five)
(7x²+3x³+4x5)
7x²+3x³+4x5
(7x²+3x³+4x⁵)
7x²+3x³+4x^5
(7x²+3x³+4x^5)dx
Similar expressions
(7x²-3x³+4x^5)
(7x²+3x³-4x^5)

Integral of (7x²+3x³+4x^5) dx

The solution

You have entered [src]

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

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

Integral(7*x^2 + 3*x^3 + 4*x^5, (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:
  
  $\int 4 x^{5}\, dx = 4 \int x^{5}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{5}\, dx = \frac{x^{6}}{6}$
  So, the result is: $\frac{2 x^{6}}{3}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x^{3}\, dx = 3 \int x^{3}\, dx$
    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: $\frac{3 x^{4}}{4}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 7 x^{2}\, dx = 7 \int x^{2}\, dx$
    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: $\frac{7 x^{3}}{3}$
  The result is: $\frac{3 x^{4}}{4} + \frac{7 x^{3}}{3}$
The result is: $\frac{2 x^{6}}{3} + \frac{3 x^{4}}{4} + \frac{7 x^{3}}{3}$
Now simplify:

$\frac{x^{3} \left(8 x^{3} + 9 x + 28\right)}{12}$
Add the constant of integration:

$\frac{x^{3} \left(8 x^{3} + 9 x + 28\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(8 x^{3} + 9 x + 28\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                  6      4      3
 | /   2      3      5\          2*x    3*x    7*x 
 | \7*x  + 3*x  + 4*x / dx = C + ---- + ---- + ----
 |                                3      4      3  
/

$$\int \left(4 x^{5} + \left(3 x^{3} + 7 x^{2}\right)\right)\, dx = C + \frac{2 x^{6}}{3} + \frac{3 x^{4}}{4} + \frac{7 x^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

15/4

$$\frac{15}{4}$$

15/4

$$\frac{15}{4}$$

15/4

Numerical answer [src]

3.75

3.75

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

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Identical expressions

Similar expressions

Integral of (7x²+3x³+4x^5) dx

Limits of integration:

The graph:

Piecewise:

The solution