Mister Exam

Other calculators

Solving integrals/ 1/(x+y)

Integral of 1/(x+y) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let u=x+yu = x + y.

    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+y)\log{\left(x + y \right)}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                         
 |                          
 |   1                      
 | ----- dx = C + log(x + y)
 | x + y                    
 |                          
/
∫1x+y dx=C+log⁡(x+y)\int \frac{1}{x + y}\, dx = C + \log{\left(x + y \right)}
Simplify
The answer [src] 
-log(y) + log(1 + y)
−log⁡(y)+log⁡(y+1)- \log{\left(y \right)} + \log{\left(y + 1 \right)} 
=
= 
-log(y) + log(1 + y)
−log⁡(y)+log⁡(y+1)- \log{\left(y \right)} + \log{\left(y + 1 \right)} 
-log(y) + log(1 + y)

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

    © Mister Exam – Calculator