Mister Exam

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Integral of d{x}:
Integral of cosx
Integral of (3-sin(x))/(2cos(x)+3tan(x))
Integral of (x-4)/x^3
Integral of x^2cos3xdx
Identical expressions
dy/e^(three *y)
dy divide by e to the power of (3 multiply by y)
dy divide by e to the power of (three multiply by y)
dy/e(3*y)
dy/e3*y
dy/e^(3y)
dy/e(3y)
dy/e3y
dy/e^3y
dy divide by e^(3*y)

Integral of dy/e^(3*y) dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{1}{e^{3 y}}\, dy$$

Integral(1/(E^(3*y)), (y, 0, 1))

Detail solution

Let $u = e^{3 y}$ .

Then let $du = 3 e^{3 y} dy$ and substitute $\frac{du}{3}$ :

$\int \frac{1}{3 u^{2}}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u^{2}}\, du = \frac{\int \frac{1}{u^{2}}\, du}{3}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{u^{2}}\, du = - \frac{1}{u}$
  So, the result is: $- \frac{1}{3 u}$
Now substitute $u$ back in:

$- \frac{e^{- 3 y}}{3}$
Add the constant of integration:

$- \frac{e^{- 3 y}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{e^{- 3 y}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   
 |                -3*y
 |  1            e    
 | ---- dy = C - -----
 |  3*y            3  
 | E                  
 |                    
/

$$\int \frac{1}{e^{3 y}}\, dy = C - \frac{e^{- 3 y}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     -3
1   e  
- - ---
3    3

$$\frac{1}{3} - \frac{1}{3 e^{3}}$$

     -3
1   e  
- - ---
3    3

$$\frac{1}{3} - \frac{1}{3 e^{3}}$$

1/3 - exp(-3)/3

Numerical answer [src]

0.316737643877379

0.316737643877379

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

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Identical expressions

Integral of dy/e^(3*y) dx

Limits of integration:

The graph:

Piecewise:

The solution