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Identical expressions
five x^5-6x+ seven
5x to the power of 5 minus 6x plus 7
five x to the power of 5 minus 6x plus seven
5x5-6x+7
5x⁵-6x+7
5x^5-6x+7dx
Similar expressions
5x^5+6x+7
5x^5-6x-7

Solving integrals/ 5x^5-6x+7

Integral of 5x^5-6x+7 dx

The solution

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  1                    
  /                    
 |                     
 |  /   5          \   
 |  \5*x  - 6*x + 7/ dx
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(5 x^{5} - 6 x + 7\right)\, dx$$

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

$\frac{x \left(5 x^{5} - 18 x + 42\right)}{6}$
Add the constant of integration:

$\frac{x \left(5 x^{5} - 18 x + 42\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(5 x^{5} - 18 x + 42\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{5\,x^6}\over{6}}-3\,x^2+7\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

29/6

$${{29}\over{6}}$$

29/6

$$\frac{29}{6}$$

Simplify

Numerical answer [src]

4.83333333333333

4.83333333333333

The graph

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

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Integral of 5x^5-6x+7 dx

Limits of integration:

The graph:

Piecewise:

The solution