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x^3sqrt(two +x^ four)
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Similar expressions
x^3sqrt(2-x^4)

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

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

The solution

You have entered [src]

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

$$\int\limits_{0}^{1} x^{3} \sqrt{x^{4} + 2}\, dx$$

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

Detail solution

Let $u = x^{4} + 2$ .

Then let $du = 4 x^{3} dx$ and substitute $\frac{du}{4}$ :

$\int \frac{\sqrt{u}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sqrt{u}\, du = \frac{\int \sqrt{u}\, du}{4}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
  So, the result is: $\frac{u^{\frac{3}{2}}}{6}$
Now substitute $u$ back in:

$\frac{\left(x^{4} + 2\right)^{\frac{3}{2}}}{6}$
Add the constant of integration:

$\frac{\left(x^{4} + 2\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}$

The answer is:

$\frac{\left(x^{4} + 2\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                 3/2
 |       ________          /     4\   
 |  3   /      4           \2 + x /   
 | x *\/  2 + x   dx = C + -----------
 |                              6     
/

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

Simplify

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Plot the graph f(x)

The answer [src]

  ___     ___
\/ 3    \/ 2 
----- - -----
  2       3

$$- \frac{\sqrt{2}}{3} + \frac{\sqrt{3}}{2}$$

  ___     ___
\/ 3    \/ 2 
----- - -----
  2       3

$$- \frac{\sqrt{2}}{3} + \frac{\sqrt{3}}{2}$$

sqrt(3)/2 - sqrt(2)/3

Numerical answer [src]

0.394620882993407

0.394620882993407

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^3sqrt(2+x^4) dx

Limits of integration:

The graph:

Piecewise:

The solution