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Identical expressions
x/(sqrt(x^ two + forty-nine))
x divide by ( square root of (x squared plus 49))
x divide by ( square root of (x to the power of two plus forty minus nine))
x/(√(x^2+49))
x/(sqrt(x2+49))
x/sqrtx2+49
x/(sqrt(x²+49))
x/(sqrt(x to the power of 2+49))
x/sqrtx^2+49
x divide by (sqrt(x^2+49))
x/(sqrt(x^2+49))dx
Similar expressions
x/(sqrt(x^2-49))

Integral of x/(sqrt(x^2+49)) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |       x         
 |  ------------ dx
 |     _________   
 |    /  2         
 |  \/  x  + 49    
 |                 
/                  
0

$$\int\limits_{0}^{1} \frac{x}{\sqrt{x^{2} + 49}}\, dx$$

Integral(x/sqrt(x^2 + 49), (x, 0, 1))

Detail solution

Let $u = \sqrt{x^{2} + 49}$ .

Then let $du = \frac{x dx}{\sqrt{x^{2} + 49}}$ and substitute $du$ :

$\int 1\, du$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, du = u$
Now substitute $u$ back in:

$\sqrt{x^{2} + 49}$
Now simplify:

$\sqrt{x^{2} + 49}$
Add the constant of integration:

$\sqrt{x^{2} + 49}+ \mathrm{constant}$

The answer is:

$\sqrt{x^{2} + 49}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                          _________
 |      x                  /  2      
 | ------------ dx = C + \/  x  + 49 
 |    _________                      
 |   /  2                            
 | \/  x  + 49                       
 |                                   
/

$$\int \frac{x}{\sqrt{x^{2} + 49}}\, dx = C + \sqrt{x^{2} + 49}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         ___
-7 + 5*\/ 2

$$-7 + 5 \sqrt{2}$$

         ___
-7 + 5*\/ 2

$$-7 + 5 \sqrt{2}$$

-7 + 5*sqrt(2)

Numerical answer [src]

0.0710678118654752

0.0710678118654752

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

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Identical expressions

Similar expressions

Integral of x/(sqrt(x^2+49)) dx

Limits of integration:

The graph:

Piecewise:

The solution