Mister Exam

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How to use it?
Integral of d{x}:
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Integral of 1÷(x^2-1)
Integral of e^x/(e^(2*x)+1)
Graphing y =:
x^3+8
Canonical form:
x^3+8
Factor polynomial:
x^3+8
Identical expressions
x^ three + eight
x cubed plus 8
x to the power of three plus eight
x3+8
x³+8
x to the power of 3+8
x^3+8dx
Similar expressions
x^3-8

Solving integrals/ x^3+8

Integral of x^3+8 dx

The solution

You have entered [src]

  1            
  /            
 |             
 |  / 3    \   
 |  \x  + 8/ dx
 |             
/              
0

$$\int\limits_{0}^{1} \left(x^{3} + 8\right)\, dx$$

Integral(x^3 + 8, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 8\, dx = 8 x$
The result is: $\frac{x^{4}}{4} + 8 x$
Now simplify:

$\frac{x \left(x^{3} + 32\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} + 32\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} + 32\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                          4
 | / 3    \                x 
 | \x  + 8/ dx = C + 8*x + --
 |                         4 
/

$$\int \left(x^{3} + 8\right)\, dx = C + \frac{x^{4}}{4} + 8 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

33/4

$$\frac{33}{4}$$

33/4

$$\frac{33}{4}$$

33/4

Numerical answer [src]

8.25

8.25

The graph

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

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Identical expressions

Similar expressions

Integral of x^3+8 dx

Limits of integration:

The graph:

Piecewise:

The solution