Mister Exam

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How to use it?
Integral of d{x}:
Integral of x/(1+x)
Integral of sin^3xcos^5x
Integral of e^(x^2)dx
Integral of (sin(x)^2)/(cos(x)^4)
Derivative of:
2*x^3
2*x^3
Limit of the function:
2*x^3
Identical expressions
two *x^ three
2 multiply by x cubed
two multiply by x to the power of three
2*x3
2*x³
2*x to the power of 3
2x^3
2x3
2*x^3dx
Similar expressions
32x^3-4x+
x^5+2x^3-5x+3
2x^3-6x^2-4x
1/(sqrt(1-4x^2)*arcsin(2x)^3)

Solving integrals/ 2*x^3

Integral of 2*x^3 dx

The solution

You have entered [src]

$$\int\limits_{0}^{2} 2 x^{3}\, dx$$

Integral(2*x^3, (x, 0, 2))

Detail solution

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: $\frac{x^{4}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int 2 x^{3}\, dx = C + \frac{x^{4}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$8$$

=

$$8$$

Numerical answer [src]

8.0

8.0

The graph

Integral of 2*x^3 dx

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