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Integral of d{x}:
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Integral of x²+2x
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Identical expressions
(x^ two + four)^ three
(x squared plus 4) cubed
(x to the power of two plus four) to the power of three
(x2+4)3
x2+43
(x²+4)³
(x to the power of 2+4) to the power of 3
x^2+4^3
(x^2+4)^3dx
Similar expressions
(x^2-4)^3

Solving integrals/ (x^2+4)^3

Integral of (x^2+4)^3 dx

The solution

You have entered [src]

  1             
  /             
 |              
 |          3   
 |  / 2    \    
 |  \x  + 4/  dx
 |              
/               
0

$$\int\limits_{0}^{1} \left(x^{2} + 4\right)^{3}\, dx$$

Integral((x^2 + 4)^3, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x^{2} + 4\right)^{3} = x^{6} + 12 x^{4} + 48 x^{2} + 64$
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:
  
  $\int 12 x^{4}\, dx = 12 \int x^{4}\, dx$
  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: $\frac{12 x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 48 x^{2}\, dx = 48 \int x^{2}\, dx$
  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: $16 x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 64\, dx = 64 x$
The result is: $\frac{x^{7}}{7} + \frac{12 x^{5}}{5} + 16 x^{3} + 64 x$
Now simplify:

$\frac{x \left(5 x^{6} + 84 x^{4} + 560 x^{2} + 2240\right)}{35}$
Add the constant of integration:

$\frac{x \left(5 x^{6} + 84 x^{4} + 560 x^{2} + 2240\right)}{35}+ \mathrm{constant}$

The answer is:

$\frac{x \left(5 x^{6} + 84 x^{4} + 560 x^{2} + 2240\right)}{35}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                             
 |         3                          7       5
 | / 2    \               3          x    12*x 
 | \x  + 4/  dx = C + 16*x  + 64*x + -- + -----
 |                                   7      5  
/

$$\int \left(x^{2} + 4\right)^{3}\, dx = C + \frac{x^{7}}{7} + \frac{12 x^{5}}{5} + 16 x^{3} + 64 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

2889
----
 35

$$\frac{2889}{35}$$

2889
----
 35

$$\frac{2889}{35}$$

2889/35

Numerical answer [src]

82.5428571428571

82.5428571428571

The graph

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

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Integral of (x^2+4)^3 dx

Limits of integration:

The graph:

Piecewise:

The solution