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Integral of d{x}:
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Integral of x*dx/(x^2+1)
Integral of x^3*exp(x^2)
Derivative of:
(x^2+1)^2
Identical expressions
(x^ two + one)^ two
(x squared plus 1) squared
(x to the power of two plus one) to the power of two
(x2+1)2
x2+12
(x²+1)²
(x to the power of 2+1) to the power of 2
x^2+1^2
(x^2+1)^2dx
Similar expressions
(x^2-1)^2

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Rewrite the integrand:

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

$\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x+ \mathrm{constant}$

The answer is:

$\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

28
--
15

$$\frac{28}{15}$$

28
--
15

$$\frac{28}{15}$$

28/15

Numerical answer [src]

1.86666666666667

1.86666666666667

The graph

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution