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Identical expressions
- one /(sqrt(3x+ four))
minus 1 divide by ( square root of (3x plus 4))
minus one divide by ( square root of (3x plus four))
-1/(√(3x+4))
-1/sqrt3x+4
-1 divide by (sqrt(3x+4))
-1/(sqrt(3x+4))dx
Similar expressions
-1/(sqrt(3x-4))
1/(sqrt(3x+4))

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

The solution

You have entered [src]

  0               
  /               
 |                
 |      -1        
 |  ----------- dx
 |    _________   
 |  \/ 3*x + 4    
 |                
/                 
-1

$$\int\limits_{-1}^{0} \left(- \frac{1}{\sqrt{3 x + 4}}\right)\, dx$$

Integral(-1/sqrt(3*x + 4), (x, -1, 0))

Detail solution

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

$\int \left(- \frac{1}{\sqrt{3 x + 4}}\right)\, dx = - \int \frac{1}{\sqrt{3 x + 4}}\, dx$
1. Let $u = \sqrt{3 x + 4}$ .
  
  Then let $du = \frac{3 dx}{2 \sqrt{3 x + 4}}$ and substitute $\frac{2 du}{3}$ :
  
  $\int \frac{2}{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $\frac{2 u}{3}$
  Now substitute $u$ back in:
  
  $\frac{2 \sqrt{3 x + 4}}{3}$
So, the result is: $- \frac{2 \sqrt{3 x + 4}}{3}$
Now simplify:

$- \frac{2 \sqrt{3 x + 4}}{3}$
Add the constant of integration:

$- \frac{2 \sqrt{3 x + 4}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{2 \sqrt{3 x + 4}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                          _________
 |     -1               2*\/ 3*x + 4 
 | ----------- dx = C - -------------
 |   _________                3      
 | \/ 3*x + 4                        
 |                                   
/

$$\int \left(- \frac{1}{\sqrt{3 x + 4}}\right)\, dx = C - \frac{2 \sqrt{3 x + 4}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2/3

$$- \frac{2}{3}$$

-2/3

$$- \frac{2}{3}$$

-2/3

Numerical answer [src]

-0.666666666666667

-0.666666666666667

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

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

Limits of integration:

The graph:

Piecewise:

The solution