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

Integral of 1/(x+3) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |    1     
 |  ----- dx
 |  x + 3   
 |          
/           
0
∫011x+3 dx\int\limits_{0}^{1} \frac{1}{x + 3}\, dx 
Integral(1/(x + 3), (x, 0, 1))
Detail solution

  1. Let u=x+3u = x + 3.

    Then let du=dxdu = dx and substitute dudu:

    ∫1u du\int \frac{1}{u}\, du

    1. The integral of 1u\frac{1}{u} is log⁡(u)\log{\left(u \right)}.

    Now substitute uu back in:

    log⁡(x+3)\log{\left(x + 3 \right)}

  2. Now simplify:

    log⁡(x+3)\log{\left(x + 3 \right)}

  3. Add the constant of integration:

    log⁡(x+3)+constant\log{\left(x + 3 \right)}+ \mathrm{constant}

The answer is:

log⁡(x+3)+constant\log{\left(x + 3 \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                         
 |                          
 |   1                      
 | ----- dx = C + log(x + 3)
 | x + 3                    
 |                          
/
∫1x+3 dx=C+log⁡(x+3)\int \frac{1}{x + 3}\, dx = C + \log{\left(x + 3 \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
-log(3) + log(4)
−log⁡(3)+log⁡(4)- \log{\left(3 \right)} + \log{\left(4 \right)} 
=
= 
-log(3) + log(4)
−log⁡(3)+log⁡(4)- \log{\left(3 \right)} + \log{\left(4 \right)} 
-log(3) + log(4)
Numerical answer [src] 
0.287682072451781
0.287682072451781
The graph
Integral of 1/(x+3) dx

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

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