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Identical expressions
(ten *(x^ five))-x+(three /x)
(10 multiply by (x to the power of 5)) minus x plus (3 divide by x)
(ten multiply by (x to the power of five)) minus x plus (three divide by x)
(10*(x5))-x+(3/x)
10*x5-x+3/x
(10*(x⁵))-x+(3/x)
(10(x^5))-x+(3/x)
(10(x5))-x+(3/x)
10x5-x+3/x
10x^5-x+3/x
(10*(x^5))-x+(3 divide by x)
(10*(x^5))-x+(3/x)dx
Similar expressions
(10*(x^5))-x-(3/x)
(10*(x^5))+x+(3/x)

Integral of (10*(x^5))-x+(3/x) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /    5       3\   
 |  |10*x  - x + -| dx
 |  \            x/   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(10 x^{5} - x\right) + \frac{3}{x}\right)\, dx$$

Integral(10*x^5 - x + 3/x, (x, 0, 1))

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:
    
    $\int 10 x^{5}\, dx = 10 \int x^{5}\, dx$
    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: $\frac{5 x^{6}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- x\right)\, dx = - \int x\, dx$
    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: $- \frac{x^{2}}{2}$
  The result is: $\frac{5 x^{6}}{3} - \frac{x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3}{x}\, dx = 3 \int \frac{1}{x}\, dx$
  1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  So, the result is: $3 \log{\left(x \right)}$
The result is: $\frac{5 x^{6}}{3} - \frac{x^{2}}{2} + 3 \log{\left(x \right)}$
Add the constant of integration:

$\frac{5 x^{6}}{3} - \frac{x^{2}}{2} + 3 \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{5 x^{6}}{3} - \frac{x^{2}}{2} + 3 \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                             
 |                                      2      6
 | /    5       3\                     x    5*x 
 | |10*x  - x + -| dx = C + 3*log(x) - -- + ----
 | \            x/                     2     3  
 |                                              
/

$$\int \left(\left(10 x^{5} - x\right) + \frac{3}{x}\right)\, dx = C + \frac{5 x^{6}}{3} - \frac{x^{2}}{2} + 3 \log{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

133.438005068645

133.438005068645

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

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Integral of (10*(x^5))-x+(3/x) dx

Limits of integration:

The graph:

Piecewise:

The solution