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

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

The solution

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

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

Integral(sqrt(x) + 3*x^3 - 2, (x, 0, 2))

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

        ___
    4*\/ 2 
8 + -------
       3

$$\frac{4 \sqrt{2}}{3} + 8$$

        ___
    4*\/ 2 
8 + -------
       3

$$\frac{4 \sqrt{2}}{3} + 8$$

8 + 4*sqrt(2)/3

Numerical answer [src]

9.88561808316413

9.88561808316413

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

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

Limits of integration:

The graph:

Piecewise:

The solution