Mister Exam

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Integral of d{x}:
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Integral of cos(5x)
Identical expressions
(sqrt(two x)+x^(three /2))
( square root of (2x) plus x to the power of (3 divide by 2))
( square root of (two x) plus x to the power of (three divide by 2))
(√(2x)+x^(3/2))
(sqrt(2x)+x(3/2))
sqrt2x+x3/2
sqrt2x+x^3/2
(sqrt(2x)+x^(3 divide by 2))
(sqrt(2x)+x^(3/2))dx
Similar expressions
(sqrt(2x)-x^(3/2))

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

The solution

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  8                    
  /                    
 |                     
 |  /  _____    3/2\   
 |  \\/ 2*x  + x   / dx
 |                     
/                      
0

$$\int\limits_{0}^{8} \left(x^{\frac{3}{2}} + \sqrt{2 x}\right)\, dx$$

Integral(sqrt(2*x) + x^(3/2), (x, 0, 8))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{\frac{3}{2}}\, dx = \frac{2 x^{\frac{5}{2}}}{5}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{2 \sqrt{2} x^{\frac{3}{2}}}{3}$
The result is: $\frac{2 x^{\frac{5}{2}}}{5} + \frac{2 \sqrt{2} x^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{2 x^{\frac{3}{2}} \left(3 x + 5 \sqrt{2}\right)}{15}$
Add the constant of integration:

$\frac{2 x^{\frac{3}{2}} \left(3 x + 5 \sqrt{2}\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{2 x^{\frac{3}{2}} \left(3 x + 5 \sqrt{2}\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

           ___
64   256*\/ 2 
-- + ---------
3        5

$$\frac{64}{3} + \frac{256 \sqrt{2}}{5}$$

           ___
64   256*\/ 2 
-- + ---------
3        5

$$\frac{64}{3} + \frac{256 \sqrt{2}}{5}$$

64/3 + 256*sqrt(2)/5

Numerical answer [src]

93.7410677268358

93.7410677268358

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution