Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^(3*x)
Integral of 2*x/(x^2+1)
Integral of sin(5*x)
Integral of sin^2(3x)
Derivative of:
e^(3*x)
Graphing y =:
e^(3*x)
Limit of the function:
e^(3*x)
Identical expressions
e^(three *x)
e to the power of (3 multiply by x)
e to the power of (three multiply by x)
e(3*x)
e3*x
e^(3x)
e(3x)
e3x
e^3x
e^(3*x)dx
Similar expressions
x*e^3x^2+2
e^3xsen2xdx
(2x+5)e^3xdx

Solving integrals/ e^(3*x)

Integral of e^(3*x) dx

The solution

You have entered [src]

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

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

Detail solution

Let $u = 3 x$ .

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

=

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

-1/3 + exp(3)/3

Numerical answer [src]

6.36184564106256

6.36184564106256

The graph

Integral of e^(3*x) dx

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