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Integral of ex
Identical expressions
5x^ four -(three /x^ four)-(three /sqrt(x))
5x to the power of 4 minus (3 divide by x to the power of 4) minus (3 divide by square root of (x))
5x to the power of four minus (three divide by x to the power of four) minus (three divide by square root of (x))
5x^4-(3/x^4)-(3/√(x))
5x4-(3/x4)-(3/sqrt(x))
5x4-3/x4-3/sqrtx
5x⁴-(3/x⁴)-(3/sqrt(x))
5x^4-3/x^4-3/sqrtx
5x^4-(3 divide by x^4)-(3 divide by sqrt(x))
5x^4-(3/x^4)-(3/sqrt(x))dx
Similar expressions
5x^4-(3/x^4)+(3/sqrt(x))
5x^4+(3/x^4)-(3/sqrt(x))

Solving integrals/ 5x^4-(3/x^4)-(3/sqrt(x))

Integral of 5x^4-(3/x^4)-(3/sqrt(x)) dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |  /   4   3      3  \   
 |  |5*x  - -- - -----| dx
 |  |        4     ___|   
 |  \       x    \/ x /   
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(\left(5 x^{4} - \frac{3}{x^{4}}\right) - \frac{3}{\sqrt{x}}\right)\, dx$$

Integral(5*x^4 - 3/x^4 - 3/sqrt(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:
    
    $\int 5 x^{4}\, dx = 5 \int x^{4}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{4}\, dx = \frac{x^{5}}{5}$
    So, the result is: $x^{5}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{3}{x^{4}}\right)\, dx = - 3 \int \frac{1}{x^{4}}\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $- \frac{1}{3 x^{3}}$
    So, the result is: $\frac{1}{x^{3}}$
  The result is: $x^{5} + \frac{1}{x^{3}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{3}{\sqrt{x}}\right)\, dx = - 3 \int \frac{1}{\sqrt{x}}\, dx$
  1. Let $u = \sqrt{x}$ .
    
    Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $2 du$ :
    
    $\int 2\, du$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\text{False}$
      1. The integral of a constant is the constant times the variable of integration:
        
        $\int 1\, du = u$
      So, the result is: $2 u$
    Now substitute $u$ back in:
    
    $2 \sqrt{x}$
  So, the result is: $- 6 \sqrt{x}$
The result is: $- 6 \sqrt{x} + x^{5} + \frac{1}{x^{3}}$
Now simplify:

$\frac{- 6 x^{\frac{7}{2}} + x^{8} + 1}{x^{3}}$
Add the constant of integration:

$\frac{- 6 x^{\frac{7}{2}} + x^{8} + 1}{x^{3}}+ \mathrm{constant}$

The answer is:

$\frac{- 6 x^{\frac{7}{2}} + x^{8} + 1}{x^{3}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 | /   4   3      3  \          1     5       ___
 | |5*x  - -- - -----| dx = C + -- + x  - 6*\/ x 
 | |        4     ___|           3               
 | \       x    \/ x /          x                
 |                                               
/

$$\int \left(\left(5 x^{4} - \frac{3}{x^{4}}\right) - \frac{3}{\sqrt{x}}\right)\, dx = C - 6 \sqrt{x} + x^{5} + \frac{1}{x^{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Numerical answer [src]

-2.34429336733757e+57

-2.34429336733757e+57

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

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Integral of 5x^4-(3/x^4)-(3/sqrt(x)) dx

Limits of integration:

The graph:

Piecewise:

The solution