Mister Exam

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Integral of d{x}:
Integral of e^(x^2)
Integral of e^(-x)
Integral of sin(x)^3
Integral of cos(x/2)
Derivative of:
(x^2+1)^3
Identical expressions
(x^ two + one)^ three
(x squared plus 1) cubed
(x to the power of two plus one) to the power of three
(x2+1)3
x2+13
(x²+1)³
(x to the power of 2+1) to the power of 3
x^2+1^3
(x^2+1)^3dx
Similar expressions
(x^2-1)^3

Integral of (x^2+1)^3 dx

The solution

You have entered [src]

  4/5            
   /             
  |              
  |          3   
  |  / 2    \    
  |  \x  + 1/  dx
  |              
 /               
1/10

$$\int\limits_{\frac{1}{10}}^{\frac{4}{5}} \left(x^{2} + 1\right)^{3}\, dx$$

Integral((x^2 + 1)^3, (x, 1/10, 4/5))

Detail solution

Rewrite the integrand:

$\left(x^{2} + 1\right)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{6}\, dx = \frac{x^{7}}{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x^{4}\, dx = 3 \int x^{4}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  So, the result is: $\frac{3 x^{5}}{5}$
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: $x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{7}}{7} + \frac{3 x^{5}}{5} + x^{3} + x$
Add the constant of integration:

$\frac{x^{7}}{7} + \frac{3 x^{5}}{5} + x^{3} + x+ \mathrm{constant}$

The answer is:

$\frac{x^{7}}{7} + \frac{3 x^{5}}{5} + x^{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                      
 |         3                    7      5
 | / 2    \                3   x    3*x 
 | \x  + 1/  dx = C + x + x  + -- + ----
 |                             7     5  
/

$$\int \left(x^{2} + 1\right)^{3}\, dx = C + \frac{x^{7}}{7} + \frac{3 x^{5}}{5} + x^{3} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

14375613
--------
10000000

$$\frac{14375613}{10000000}$$

14375613
--------
10000000

$$\frac{14375613}{10000000}$$

14375613/10000000

Numerical answer [src]

1.4375613

1.4375613

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

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Identical expressions

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Integral of (x^2+1)^3 dx

Limits of integration:

The graph:

Piecewise:

The solution