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Integral of x-2
Derivative of:
(x^2+1)^4
Identical expressions
(x^ two + one)^ four
(x squared plus 1) to the power of 4
(x to the power of two plus one) to the power of four
(x2+1)4
x2+14
(x²+1)⁴
(x to the power of 2+1) to the power of 4
x^2+1^4
(x^2+1)^4dx
Similar expressions
(x^2-1)^4

Solving integrals/ (x^2+1)^4

Integral of (x^2+1)^4 dx

The solution

You have entered [src]

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

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

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

Detail solution

Rewrite the integrand:

$\left(x^{2} + 1\right)^{4} = x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 1$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{8}\, dx = \frac{x^{9}}{9}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x^{6}\, dx = 4 \int x^{6}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{6}\, dx = \frac{x^{7}}{7}$
  So, the result is: $\frac{4 x^{7}}{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 6 x^{4}\, dx = 6 \int x^{4}\, dx$
  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: $\frac{6 x^{5}}{5}$
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:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{9}}{9} + \frac{4 x^{7}}{7} + \frac{6 x^{5}}{5} + \frac{4 x^{3}}{3} + x$
Now simplify:

$\frac{x \left(35 x^{8} + 180 x^{6} + 378 x^{4} + 420 x^{2} + 315\right)}{315}$
Add the constant of integration:

$\frac{x \left(35 x^{8} + 180 x^{6} + 378 x^{4} + 420 x^{2} + 315\right)}{315}+ \mathrm{constant}$

The answer is:

$\frac{x \left(35 x^{8} + 180 x^{6} + 378 x^{4} + 420 x^{2} + 315\right)}{315}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 |         4               9      3      7      5
 | / 2    \               x    4*x    4*x    6*x 
 | \x  + 1/  dx = C + x + -- + ---- + ---- + ----
 |                        9     3      7      5  
/

$$\int \left(x^{2} + 1\right)^{4}\, dx = C + \frac{x^{9}}{9} + \frac{4 x^{7}}{7} + \frac{6 x^{5}}{5} + \frac{4 x^{3}}{3} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1328
----
315

$$\frac{1328}{315}$$

1328
----
315

$$\frac{1328}{315}$$

1328/315

Numerical answer [src]

4.21587301587302

4.21587301587302

The graph

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

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Integral of (x^2+1)^4 dx

Limits of integration:

The graph:

Piecewise:

The solution