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Integral of d{x}:
Integral of x^(-1/2)
Integral of 1/sqrt(1+u^2)
Integral of sinx/cos2x
Integral of e^(x/3)
Derivative of:
e^(x/3)
Limit of the function:
e^(x/3)
Identical expressions
e^(x/ three)
e to the power of (x divide by 3)
e to the power of (x divide by three)
e(x/3)
ex/3
e^x/3
e^(x divide by 3)
e^(x/3)dx

Solving integrals/ e^(x/3)

Integral of e^(x/3) dx

The solution

You have entered [src]

\int\limits_{0}^{1} e^{\frac{x}{3}}\, dx

Integral(E^(x/3), (x, 0, 1))

Detail solution

Let $u = \frac{x}{3}$ .

Then let $du = \frac{dx}{3}$ and substitute $3 du$ :

$\int 3 e^{u}\, du$
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: $3 e^{u}$
Now substitute $u$ back in:

$3 e^{\frac{x}{3}}$
Now simplify:

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

$3 e^{\frac{x}{3}}+ \mathrm{constant}$

The answer is:

3 e^{\frac{x}{3}}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                
 |                 
 |  x             x
 |  -             -
 |  3             3
 | E  dx = C + 3*e 
 |                 
/

\int e^{\frac{x}{3}}\, dx = C + 3 e^{\frac{x}{3}}

Simplify

The graph

Plot the graph f(x)

The answer [src]

        1/3
-3 + 3*e

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

=

        1/3
-3 + 3*e

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

-3 + 3*exp(1/3)

Numerical answer [src]

1.18683727525827

1.18683727525827

The graph

Integral of e^(x/3) dx

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