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Identical expressions
(one / eight)*x^ two + one
(1 divide by 8) multiply by x squared plus 1
(one divide by eight) multiply by x to the power of two plus one
(1/8)*x2+1
1/8*x2+1
(1/8)*x²+1
(1/8)*x to the power of 2+1
(1/8)x^2+1
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1/8x2+1
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(1/8)*x^2+1dx
Similar expressions
(1/8)*x^2-1

Integral of (1/8)*x^2+1 dx

The solution

You have entered [src]

  1            
  /            
 |             
 |  / 2    \   
 |  |x     |   
 |  |-- + 1| dx
 |  \8     /   
 |             
/              
0

$$\int\limits_{0}^{1} \left(\frac{x^{2}}{8} + 1\right)\, dx$$

Integral(x^2/8 + 1, (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:
  
  $\int \frac{x^{2}}{8}\, dx = \frac{\int x^{2}\, dx}{8}$
  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: $\frac{x^{3}}{24}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{3}}{24} + x$
Add the constant of integration:

$\frac{x^{3}}{24} + x+ \mathrm{constant}$

The answer is:

$\frac{x^{3}}{24} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                         
 | / 2    \               3
 | |x     |              x 
 | |-- + 1| dx = C + x + --
 | \8     /              24
 |                         
/

$$\int \left(\frac{x^{2}}{8} + 1\right)\, dx = C + \frac{x^{3}}{24} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

25
--
24

$$\frac{25}{24}$$

25
--
24

$$\frac{25}{24}$$

25/24

Numerical answer [src]

1.04166666666667

1.04166666666667

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

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Integral of (1/8)*x^2+1 dx

Limits of integration:

The graph:

Piecewise:

The solution