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x³+2x/√xdx
x³ plus 2x divide by √xdx
x³+2x divide by √xdx
Similar expressions
x³-2x/√xdx

Integral of x³+2x/√xdx dx

The solution

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  0                
  /                
 |                 
 |  / 3    2*x \   
 |  |x  + -----| dx
 |  |       ___|   
 |  \     \/ x /   
 |                 
/                  
0

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

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

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
1. Let $u = \sqrt{x}$ .
  
  Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $4 du$ :
  
  $\int 4 u^{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u^{2}\, du = 4 \int u^{2}\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u^{2}\, du = \frac{u^{3}}{3}$
    So, the result is: $\frac{4 u^{3}}{3}$
  Now substitute $u$ back in:
  
  $\frac{4 x^{\frac{3}{2}}}{3}$
The result is: $\frac{4 x^{\frac{3}{2}}}{3} + \frac{x^{4}}{4}$
Add the constant of integration:

$\frac{4 x^{\frac{3}{2}}}{3} + \frac{x^{4}}{4}+ \mathrm{constant}$

The answer is:

$\frac{4 x^{\frac{3}{2}}}{3} + \frac{x^{4}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

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The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Similar expressions

Integral of x³+2x/√xdx dx

Limits of integration:

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Piecewise:

The solution