Integral of 1/(x+6) dx

The solution

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  1         
  /         
 |          
 |    1     
 |  ----- dx
 |  x + 6   
 |          
/           
0

$$\int\limits_{0}^{1} \frac{1}{x + 6}\, dx$$

Integral(1/(x + 6), (x, 0, 1))

Detail solution

Let $u = x + 6$ .

Then let $du = dx$ and substitute $du$ :

$\int \frac{1}{u}\, du$
1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
Now substitute $u$ back in:

$\log{\left(x + 6 \right)}$
Now simplify:

$\log{\left(x + 6 \right)}$
Add the constant of integration:

$\log{\left(x + 6 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(x + 6 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                          
 |   1                      
 | ----- dx = C + log(x + 6)
 | x + 6                    
 |                          
/

$$\int \frac{1}{x + 6}\, dx = C + \log{\left(x + 6 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(6) + log(7)

$$- \log{\left(6 \right)} + \log{\left(7 \right)}$$

-log(6) + log(7)

$$- \log{\left(6 \right)} + \log{\left(7 \right)}$$

-log(6) + log(7)

Numerical answer [src]

0.154150679827258

0.154150679827258

The graph

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

Other calculators

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Identical expressions

Similar expressions

Integral of 1/(x+6) dx

Limits of integration:

The graph:

Piecewise:

The solution