Mister Exam

Other calculators

Solving integrals/ 3^x/(log3)

Integral of 3^x/(log3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

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

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                       
 |                        
 |    x                x  
 |   3                3   
 | ------ dx = C + -------
 | log(3)             2   
 |                 log (3)
/
$$\int \frac{3^{x}}{\log{\left(3 \right)}}\, dx = \frac{3^{x}}{\log{\left(3 \right)}^{2}} + C$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   2   
-------
   2   
log (3)
$$\frac{2}{\log{\left(3 \right)}^{2}}$$ 
=
= 
   2   
-------
   2   
log (3)
$$\frac{2}{\log{\left(3 \right)}^{2}}$$ 
2/log(3)^2
Numerical answer [src] 
1.65707089938045
1.65707089938045

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

    © Mister Exam – Calculator