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Solving integrals/ e^2x+3y

You entered:

e^2x+3y

What you mean?

e^2*x + 3*y
 
e^(2*x) + 3*y
 
e^(2*x + 3)*y
 
e^(2*x + 3)*y

Integral of e^2x+3y dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

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

      1. The integral of is when :

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                          2         
 | / 2        \          3*y         2
 | \e *x + 3*y/ dy = C + ---- + x*y*e 
 |                        2           
/
$$\int \left(x e^{2} + 3 y\right)\, dy = C + x y e^{2} + \frac{3 y^{2}}{2}$$
Simplify
The answer [src] 
         2               
3*(1 - x)               2
---------- + x*(1 - x)*e 
    2
$$x \left(1 - x\right) e^{2} + \frac{3 \left(1 - x\right)^{2}}{2}$$ 
=
= 
         2               
3*(1 - x)               2
---------- + x*(1 - x)*e 
    2
$$x \left(1 - x\right) e^{2} + \frac{3 \left(1 - x\right)^{2}}{2}$$
Упростить

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

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