Mister Exam

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Derivative of:
(x^2+2)^2
Identical expressions
(x^ two + two)^ two
(x squared plus 2) squared
(x to the power of two plus two) to the power of two
(x2+2)2
x2+22
(x²+2)²
(x to the power of 2+2) to the power of 2
x^2+2^2
(x^2+2)^2dx
Similar expressions
(x^2-2)^2

Solving integrals/ (x^2+2)^2

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

The solution

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

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

Integral((x^2 + 2)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

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

$\frac{x \left(3 x^{4} + 20 x^{2} + 60\right)}{15}$
Add the constant of integration:

$\frac{x \left(3 x^{4} + 20 x^{2} + 60\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x^{4} + 20 x^{2} + 60\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                                   
 |         2                 5      3
 | / 2    \                 x    4*x 
 | \x  + 2/  dx = C + 4*x + -- + ----
 |                          5     3  
/

$$\int \left(x^{2} + 2\right)^{2}\, dx = C + \frac{x^{5}}{5} + \frac{4 x^{3}}{3} + 4 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

83
--
15

$$\frac{83}{15}$$

83
--
15

$$\frac{83}{15}$$

83/15

Numerical answer [src]

5.53333333333333

5.53333333333333

The graph

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+2)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution