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Identical expressions
(x^(- one / two))-(x^(- three / four))
(x to the power of ( minus 1 divide by 2)) minus (x to the power of ( minus 3 divide by 4))
(x to the power of ( minus one divide by two)) minus (x to the power of ( minus three divide by four))
(x(-1/2))-(x(-3/4))
x-1/2-x-3/4
x^-1/2-x^-3/4
(x^(-1 divide by 2))-(x^(-3 divide by 4))
(x^(-1/2))-(x^(-3/4))dx
Similar expressions
(x^(-1/2))+(x^(-3/4))
(x^(1/2))-(x^(-3/4))
(x^(-1/2))-(x^(3/4))

Solving integrals/ (x^(-1/2))-(x^(-3/4))

Integral of (x^(-1/2))-(x^(-3/4)) dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |  /  1      1  \   
 |  |----- - ----| dx
 |  |  ___    3/4|   
 |  \\/ x    x   /   
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(\frac{1}{\sqrt{x}} - \frac{1}{x^{\frac{3}{4}}}\right)\, dx$$

Integral(1/sqrt(x) - 1/x^(3/4), (x, 0, 1))

Detail solution

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

$- 4 \sqrt[4]{x} + 2 \sqrt{x}+ \mathrm{constant}$

The answer is:

$- 4 \sqrt[4]{x} + 2 \sqrt{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 | /  1      1  \            4 ___       ___
 | |----- - ----| dx = C - 4*\/ x  + 2*\/ x 
 | |  ___    3/4|                           
 | \\/ x    x   /                           
 |                                          
/

$$\int \left(\frac{1}{\sqrt{x}} - \frac{1}{x^{\frac{3}{4}}}\right)\, dx = C - 4 \sqrt[4]{x} + 2 \sqrt{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2

$$-2$$

-2

$$-2$$

-2

Numerical answer [src]

-1.99993476844119

-1.99993476844119

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

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Identical expressions

Similar expressions

Integral of (x^(-1/2))-(x^(-3/4)) dx

Limits of integration:

The graph:

Piecewise:

The solution