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Integral of d{x}:
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Identical expressions
5sinsqrtx/sqrtx
5 sinus of square root of x divide by square root of x
5sin√x/√x
5sinsqrtx divide by sqrtx
5sinsqrtx/sqrtxdx

Integral of 5sinsqrtx/sqrtx dx

The solution

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  0                
  /                
 |                 
 |       /  ___\   
 |  5*sin\\/ x /   
 |  ------------ dx
 |       ___       
 |     \/ x        
 |                 
/                  
0

$$\int\limits_{0}^{0} \frac{5 \sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\, dx$$

Integral((5*sin(sqrt(x)))/sqrt(x), (x, 0, 0))

Detail solution

Let $u = \sqrt{x}$ .

Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $10 du$ :

$\int 10 \sin{\left(u \right)}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = 10 \int \sin{\left(u \right)}\, du$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- 10 \cos{\left(u \right)}$
Now substitute $u$ back in:

$- 10 \cos{\left(\sqrt{x} \right)}$
Add the constant of integration:

$- 10 \cos{\left(\sqrt{x} \right)}+ \mathrm{constant}$

The answer is:

$- 10 \cos{\left(\sqrt{x} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                    
 |      /  ___\                       
 | 5*sin\\/ x /                /  ___\
 | ------------ dx = C - 10*cos\\/ x /
 |      ___                           
 |    \/ x                            
 |                                    
/

$$\int \frac{5 \sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\, dx = C - 10 \cos{\left(\sqrt{x} \right)}$$

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

Integral of 5sinsqrtx/sqrtx dx

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The solution