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Identical expressions
(two *x^ one / five -2x^ one / three + five)dx
(2 multiply by x to the power of 1 divide by 5 minus 2x to the power of 1 divide by 3 plus 5)dx
(two multiply by x to the power of one divide by five minus 2x to the power of one divide by three plus five)dx
(2*x1/5-2x1/3+5)dx
2*x1/5-2x1/3+5dx
(2x^1/5-2x^1/3+5)dx
(2x1/5-2x1/3+5)dx
2x1/5-2x1/3+5dx
2x^1/5-2x^1/3+5dx
(2*x^1 divide by 5-2x^1 divide by 3+5)dx
Similar expressions
(2*x^1/5+2x^1/3+5)dx
(2*x^1/5-2x^1/3-5)dx

Integral of (2*x^1/5-2x^1/3+5)dx dx

The solution

You have entered [src]

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

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

Integral(2*x^(1/5) - 2*x^(1/3) + 5, (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:
    
    $\int 2 \sqrt[5]{x}\, dx = 2 \int \sqrt[5]{x}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \sqrt[5]{x}\, dx = \frac{5 x^{\frac{6}{5}}}{6}$
    So, the result is: $\frac{5 x^{\frac{6}{5}}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 2 \sqrt[3]{x}\right)\, dx = - 2 \int \sqrt[3]{x}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \sqrt[3]{x}\, dx = \frac{3 x^{\frac{4}{3}}}{4}$
    So, the result is: $- \frac{3 x^{\frac{4}{3}}}{2}$
  The result is: $\frac{5 x^{\frac{6}{5}}}{3} - \frac{3 x^{\frac{4}{3}}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $\frac{5 x^{\frac{6}{5}}}{3} - \frac{3 x^{\frac{4}{3}}}{2} + 5 x$
Add the constant of integration:

$\frac{5 x^{\frac{6}{5}}}{3} - \frac{3 x^{\frac{4}{3}}}{2} + 5 x+ \mathrm{constant}$

The answer is:

$\frac{5 x^{\frac{6}{5}}}{3} - \frac{3 x^{\frac{4}{3}}}{2} + 5 x+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

31/6

$$\frac{31}{6}$$

31/6

$$\frac{31}{6}$$

31/6

Numerical answer [src]

5.16666666666667

5.16666666666667

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

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Identical expressions

Similar expressions

Integral of (2*x^1/5-2x^1/3+5)dx dx

Limits of integration:

The graph:

Piecewise:

The solution