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Solving integrals/ x/sqrt(1+9*x^2)

Integral of x/sqrt(1+9*x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |        x         
 |  ------------- dx
 |     __________   
 |    /        2    
 |  \/  1 + 9*x     
 |                  
/                   
0
∫01x9x2+1 dx\int\limits_{0}^{1} \frac{x}{\sqrt{9 x^{2} + 1}}\, dx 
Integral(x/sqrt(1 + 9*x^2), (x, 0, 1))
Detail solution

  1. Let u=9x2+1u = \sqrt{9 x^{2} + 1}.

    Then let du=9xdx9x2+1du = \frac{9 x dx}{\sqrt{9 x^{2} + 1}} and substitute du9\frac{du}{9}:

    ∫19 du\int \frac{1}{9}\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      False\text{False}

      1. The integral of a constant is the constant times the variable of integration:

        ∫1 du=u\int 1\, du = u

      So, the result is: u9\frac{u}{9}

    Now substitute uu back in:

    9x2+19\frac{\sqrt{9 x^{2} + 1}}{9}

  2. Add the constant of integration:

    9x2+19+constant\frac{\sqrt{9 x^{2} + 1}}{9}+ \mathrm{constant}

The answer is:

9x2+19+constant\frac{\sqrt{9 x^{2} + 1}}{9}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          __________
 |                          /        2 
 |       x                \/  1 + 9*x  
 | ------------- dx = C + -------------
 |    __________                9      
 |   /        2                        
 | \/  1 + 9*x                         
 |                                     
/
∫x9x2+1 dx=C+9x2+19\int \frac{x}{\sqrt{9 x^{2} + 1}}\, dx = C + \frac{\sqrt{9 x^{2} + 1}}{9}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.5
Plot the graph f(x)
The answer [src] 
        ____
  1   \/ 10 
- - + ------
  9     9
−19+109- \frac{1}{9} + \frac{\sqrt{10}}{9} 
=
= 
        ____
  1   \/ 10 
- - + ------
  9     9
−19+109- \frac{1}{9} + \frac{\sqrt{10}}{9} 
-1/9 + sqrt(10)/9
Numerical answer [src] 
0.240253073352042
0.240253073352042

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

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