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Identical expressions
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Similar expressions
5x²dx/√1+x³

Integral of 5x²dx/√1-x³ dx

The solution

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

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

Integral((5*x^2)/sqrt(1) - x^3, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{3}\right)\, dx = - \int x^{3}\, dx$
  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: $- \frac{x^{4}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{5 x^{2}}{\sqrt{1}}\, dx = \int 5 x^{2}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\frac{5 x^{3}}{3}$
  So, the result is: $\frac{5 x^{3}}{3}$
The result is: $- \frac{x^{4}}{4} + \frac{5 x^{3}}{3}$
Now simplify:

$\frac{x^{3} \left(20 - 3 x\right)}{12}$
Add the constant of integration:

$\frac{x^{3} \left(20 - 3 x\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(20 - 3 x\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 | /    2     \           4      3
 | | 5*x     3|          x    5*x 
 | |----- - x | dx = C - -- + ----
 | |  ___     |          4     3  
 | \\/ 1      /                   
 |                                
/

$$\int \left(- x^{3} + \frac{5 x^{2}}{\sqrt{1}}\right)\, dx = C - \frac{x^{4}}{4} + \frac{5 x^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

17
--
12

$$\frac{17}{12}$$

17
--
12

$$\frac{17}{12}$$

17/12

Numerical answer [src]

1.41666666666667

1.41666666666667

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

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Integral of 5x²dx/√1-x³ dx

Limits of integration:

The graph:

Piecewise:

The solution