Mister Exam

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Integral of d{x}:
Integral of x^2/x
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Integral of sin3
Identical expressions
x^ one / two -3x^ two
x to the power of 1 divide by 2 minus 3x squared
x to the power of one divide by two minus 3x to the power of two
x1/2-3x2
x^1/2-3x²
x to the power of 1/2-3x to the power of 2
x^1 divide by 2-3x^2
x^1/2-3x^2dx
Similar expressions
x^1/2+3x^2

Solving integrals/ x^1/2-3x^2

Integral of x^1/2-3x^2 dx

The solution

You have entered [src]

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

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

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

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{2\,x^{{{3}\over{2}}}}\over{3}}-x^3$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/3

$$-{{1}\over{3}}$$

-1/3

$$- \frac{1}{3}$$

Упростить

Numerical answer [src]

-0.333333333333333

-0.333333333333333

The graph

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

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Integral of x^1/2-3x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution