Mister Exam

Lang:

Solving integrals/ (2/3)^x

Integral of (2/3)^x dx

You have entered [src]

$$\int\limits_{0}^{1} \left(\frac{2}{3}\right)^{x}\, dx$$

Integral((2/3)^x, (x, 0, 1))

Detail solution

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

$\int \left(\frac{2}{3}\right)^{x}\, dx = \frac{\left(\frac{2}{3}\right)^{x}}{\log{\left(\frac{2}{3} \right)}}$
Add the constant of integration:

$\frac{\left(\frac{2}{3}\right)^{x}}{\log{\left(\frac{2}{3} \right)}}+ \mathrm{constant}$

The answer is:

$\frac{\left(\frac{2}{3}\right)^{x}}{\log{\left(\frac{2}{3} \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                    x  
 |    x            2/3   
 | 2/3  dx = C + --------
 |               log(2/3)
/

$$\int \left(\frac{2}{3}\right)^{x}\, dx = \frac{\left(\frac{2}{3}\right)^{x}}{\log{\left(\frac{2}{3} \right)}} + C$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

        -1          
--------------------
3*(-log(3) + log(2))

$$- \frac{1}{3 \left(- \log{\left(3 \right)} + \log{\left(2 \right)}\right)}$$

        -1          
--------------------
3*(-log(3) + log(2))

$$- \frac{1}{3 \left(- \log{\left(3 \right)} + \log{\left(2 \right)}\right)}$$

-1/(3*(-log(3) + log(2)))

Numerical answer [src]

0.822101154125477

0.822101154125477

The graph

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