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Identical expressions
one /(sqrt(x))+ two *x^ three - seven
1 divide by ( square root of (x)) plus 2 multiply by x cubed minus 7
one divide by ( square root of (x)) plus two multiply by x to the power of three minus seven
1/(√(x))+2*x^3-7
1/(sqrt(x))+2*x3-7
1/sqrtx+2*x3-7
1/(sqrt(x))+2*x³-7
1/(sqrt(x))+2*x to the power of 3-7
1/(sqrt(x))+2x^3-7
1/(sqrt(x))+2x3-7
1/sqrtx+2x3-7
1/sqrtx+2x^3-7
1 divide by (sqrt(x))+2*x^3-7
1/(sqrt(x))+2*x^3-7dx
Similar expressions
1/(sqrt(x))-2*x^3-7
1/(sqrt(x))+2*x^3+7

Integral of 1/(sqrt(x))+2*x^3-7 dx

The solution

You have entered [src]

  1                      
  /                      
 |                       
 |  /  1        3    \   
 |  |----- + 2*x  - 7| dx
 |  |  ___           |   
 |  \\/ x            /   
 |                       
/                        
0

$$\int\limits_{0}^{1} \left(\left(2 x^{3} + \frac{1}{\sqrt{x}}\right) - 7\right)\, dx$$

Integral(1/(sqrt(x)) + 2*x^3 - 7, (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:
    
    $\int 2 x^{3}\, dx = 2 \int x^{3}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{3}\, dx = \frac{x^{4}}{4}$
    So, the result is: $\frac{x^{4}}{2}$
  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:
    
    $2 \sqrt{x}$
  The result is: $2 \sqrt{x} + \frac{x^{4}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-7\right)\, dx = - 7 x$
The result is: $2 \sqrt{x} + \frac{x^{4}}{2} - 7 x$
Add the constant of integration:

$2 \sqrt{x} + \frac{x^{4}}{2} - 7 x+ \mathrm{constant}$

The answer is:

$2 \sqrt{x} + \frac{x^{4}}{2} - 7 x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                              4                
 | /  1        3    \          x              ___
 | |----- + 2*x  - 7| dx = C + -- - 7*x + 2*\/ x 
 | |  ___           |          2                 
 | \\/ x            /                            
 |                                               
/

$$\int \left(\left(2 x^{3} + \frac{1}{\sqrt{x}}\right) - 7\right)\, dx = C + 2 \sqrt{x} + \frac{x^{4}}{2} - 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-9/2

$$- \frac{9}{2}$$

-9/2

$$- \frac{9}{2}$$

-9/2

Numerical answer [src]

-4.50000000066987

-4.50000000066987

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

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Integral of 1/(sqrt(x))+2*x^3-7 dx

Limits of integration:

The graph:

Piecewise:

The solution