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Solving integrals/ dy/(2xy+3y)

Integral of dy/(2xy+3y) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dy
 |  2*x*y + 3*y   
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{1}{2 x y + 3 y}\, dy$$ 
Integral(1/((2*x)*y + 3*y), (y, 0, 1))
Detail solution

  1. Rewrite the integrand:

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

    1. The integral of is .

    So, the result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            
 |                             
 |      1                log(y)
 | ----------- dy = C + -------
 | 2*x*y + 3*y          3 + 2*x
 |                             
/
$$\int \frac{1}{2 x y + 3 y}\, dy = C + \frac{\log{\left(y \right)}}{2 x + 3}$$
Simplify
The answer [src] 
       /   1   \
oo*sign|-------|
       \3 + 2*x/
$$\infty \operatorname{sign}{\left(\frac{1}{2 x + 3} \right)}$$ 
=
= 
       /   1   \
oo*sign|-------|
       \3 + 2*x/
$$\infty \operatorname{sign}{\left(\frac{1}{2 x + 3} \right)}$$ 
oo*sign(1/(3 + 2*x))

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

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