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Solving integrals/ 1/sqrt(3*x+1)

Integral of 1/sqrt(3*x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |    _________   
 |  \/ 3*x + 1    
 |                
/                 
0
∫0113x+1 dx\int\limits_{0}^{1} \frac{1}{\sqrt{3 x + 1}}\, dx 
Integral(1/(sqrt(3*x + 1)), (x, 0, 1))
Detail solution

  1. Let u=3x+1u = \sqrt{3 x + 1}.

    Then let du=3dx23x+1du = \frac{3 dx}{2 \sqrt{3 x + 1}} and substitute 2du3\frac{2 du}{3}:

    ∫23 du\int \frac{2}{3}\, 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: 2u3\frac{2 u}{3}

    Now substitute uu back in:

    23x+13\frac{2 \sqrt{3 x + 1}}{3}

  2. Now simplify:

    23x+13\frac{2 \sqrt{3 x + 1}}{3}

  3. Add the constant of integration:

    23x+13+constant\frac{2 \sqrt{3 x + 1}}{3}+ \mathrm{constant}

The answer is:

23x+13+constant\frac{2 \sqrt{3 x + 1}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                          _________
 |      1               2*\/ 3*x + 1 
 | ----------- dx = C + -------------
 |   _________                3      
 | \/ 3*x + 1                        
 |                                   
/
∫13x+1 dx=C+23x+13\int \frac{1}{\sqrt{3 x + 1}}\, dx = C + \frac{2 \sqrt{3 x + 1}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.02.0
Plot the graph f(x)
The answer [src] 
2/3
23\frac{2}{3} 
=
= 
2/3
23\frac{2}{3} 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667

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

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