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e^(2*x)+3
Solving integrals/ e^(2*x)+3

Integral of e^(2*x)+3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    1. Let .

      Then let and substitute :

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

        1. The integral of the exponential function is itself.

        So, the result is:

      Now substitute back in:

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

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              
 |                      2*x      
 | / 2*x    \          e         
 | \E    + 3/ dx = C + ---- + 3*x
 |                      2        
/
$$\int \left(e^{2 x} + 3\right)\, dx = C + 3 x + \frac{e^{2 x}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     2
5   e 
- + --
2   2
$$\frac{5}{2} + \frac{e^{2}}{2}$$ 
=
= 
     2
5   e 
- + --
2   2
$$\frac{5}{2} + \frac{e^{2}}{2}$$ 
5/2 + exp(2)/2
Numerical answer [src] 
6.19452804946533
6.19452804946533
The graph
Integral of e^(2*x)+3 dx

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

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