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

The solution

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 -1               
  /               
 |                
 |       1        
 |  ----------- dx
 |    _________   
 |  \/ 3*x + 4    
 |                
/                 
7

$$\int\limits_{7}^{-1} \frac{1}{\sqrt{3 x + 4}}\, dx$$

Integral(1/(sqrt(3*x + 4)), (x, 7, -1))

Detail solution

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:

$\frac{2 \sqrt{3 x + 4}}{3}$
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                        
 |                                   
/

$$\int \frac{1}{\sqrt{3 x + 4}}\, dx = C + \frac{2 \sqrt{3 x + 4}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-8/3

$$- \frac{8}{3}$$

-8/3

$$- \frac{8}{3}$$

-8/3

Numerical answer [src]

-2.66666666666667

-2.66666666666667

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