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Solving integrals/ (5^x-8)

Integral of (5^x-8) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  / x    \   
 |  \5  - 8/ dx
 |             
/              
0
$$\int\limits_{0}^{1} \left(5^{x} - 8\right)\, dx$$ 
Integral(5^x - 8, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of an exponential function is itself divided by the natural logarithm of the base.

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

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              
 |                            x  
 | / x    \                  5   
 | \5  - 8/ dx = C - 8*x + ------
 |                         log(5)
/
$$\int \left(5^{x} - 8\right)\, dx = \frac{5^{x}}{\log{\left(5 \right)}} + C - 8 x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       4   
-8 + ------
     log(5)
$$-8 + \frac{4}{\log{\left(5 \right)}}$$ 
=
= 
       4   
-8 + ------
     log(5)
$$-8 + \frac{4}{\log{\left(5 \right)}}$$ 
-8 + 4/log(5)
Numerical answer [src] 
-5.51466026176155
-5.51466026176155

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

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