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Solving integrals/ (1^(2x+2))/(3x+8)

Integral of (1^(2x+2))/(3x+8) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |   2*x + 2   
 |  1          
 |  -------- dx
 |  3*x + 8    
 |             
/              
0
$$\int\limits_{0}^{1} \frac{1^{2 x + 2}}{3 x + 8}\, dx$$ 
Integral(1^(2*x + 2)/(3*x + 8), (x, 0, 1))
Detail solution

  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 is .

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              
 |                               
 |  2*x + 2                      
 | 1                 log(3*x + 8)
 | -------- dx = C + ------------
 | 3*x + 8                3      
 |                               
/
$$\int \frac{1^{2 x + 2}}{3 x + 8}\, dx = C + \frac{\log{\left(3 x + 8 \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  log(8)   log(11)
- ------ + -------
    3         3
$$- \frac{\log{\left(8 \right)}}{3} + \frac{\log{\left(11 \right)}}{3}$$ 
=
= 
  log(8)   log(11)
- ------ + -------
    3         3
$$- \frac{\log{\left(8 \right)}}{3} + \frac{\log{\left(11 \right)}}{3}$$ 
-log(8)/3 + log(11)/3
Numerical answer [src] 
0.106151243706178
0.106151243706178

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

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