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Integral of d{x}:
Integral of x^(1/3)
Integral of sin(x)^4
Integral of cos(x)^3
Integral of (e^(x^2))
Identical expressions
exp(two *y)
exponent of (2 multiply by y)
exponent of (two multiply by y)
exp(2y)
exp2y
exp(2*y)dx

Solving integrals/ exp(2*y)

Integral of exp(2*y) dy

The solution

You have entered [src]

$$\int\limits_{-\infty}^{0} e^{2 y}\, dy$$

Integral(exp(2*y), (y, -oo, 0))

Detail solution

Let $u = 2 y$ .

Then let $du = 2 dy$ and substitute $\frac{du}{2}$ :

$\int \frac{e^{u}}{2}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $\frac{e^{u}}{2}$
Now substitute $u$ back in:

$\frac{e^{2 y}}{2}$
Add the constant of integration:

$\frac{e^{2 y}}{2}+ \mathrm{constant}$

The answer is:

$\frac{e^{2 y}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                2*y
 |  2*y          e   
 | e    dy = C + ----
 |                2  
/

$$\int e^{2 y}\, dy = C + \frac{e^{2 y}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2

$$\frac{1}{2}$$

=

1/2

$$\frac{1}{2}$$

1/2

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