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Solving integrals/ -1/(sqrt(3x+4))

Integral of -1/(sqrt(3x+4)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  0               
  /               
 |                
 |      -1        
 |  ----------- dx
 |    _________   
 |  \/ 3*x + 4    
 |                
/                 
-1
∫−10(−13x+4) dx\int\limits_{-1}^{0} \left(- \frac{1}{\sqrt{3 x + 4}}\right)\, dx 
Integral(-1/sqrt(3*x + 4), (x, -1, 0))
Detail solution

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

    ∫(−13x+4) dx=−∫13x+4 dx\int \left(- \frac{1}{\sqrt{3 x + 4}}\right)\, dx = - \int \frac{1}{\sqrt{3 x + 4}}\, dx

    1. Let u=3x+4u = \sqrt{3 x + 4}.

      Then let du=3dx23x+4du = \frac{3 dx}{2 \sqrt{3 x + 4}} 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+43\frac{2 \sqrt{3 x + 4}}{3}

    So, the result is: −23x+43- \frac{2 \sqrt{3 x + 4}}{3}

  2. Now simplify:

    −23x+43- \frac{2 \sqrt{3 x + 4}}{3}

  3. Add the constant of integration:

    −23x+43+constant- \frac{2 \sqrt{3 x + 4}}{3}+ \mathrm{constant}

The answer is:

−23x+43+constant- \frac{2 \sqrt{3 x + 4}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                          _________
 |     -1               2*\/ 3*x + 4 
 | ----------- dx = C - -------------
 |   _________                3      
 | \/ 3*x + 4                        
 |                                   
/
∫(−13x+4) dx=C−23x+43\int \left(- \frac{1}{\sqrt{3 x + 4}}\right)\, dx = C - \frac{2 \sqrt{3 x + 4}}{3}
Simplify
The graph
-1.00-0.90-0.80-0.70-0.60-0.50-0.40-0.30-0.20-0.100.00-2.00.0
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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