Tuesday, October 12, 2010

`int 3^xdx` Find the indefinite integral

Indefinite integral are written in the form of` int f(x) dx = F(x) +C`


 where: f(x) as the integrand


           F(x) as the anti-derivative function 


           C  as the arbitrary constant known as constant of integration


For the given problem `int 3^x dx `  has a integrand in a form of exponential function.


 There is basic integration formula for exponential function:


`int a^u du = a^u/(ln(a)) +C` where a is a constant.


By comparison, `a = 3` ,` u = x` , and `du =dx` .


 Applying the formula, we get:


`int 3^x dx = 3^x/(ln(3)) +C`

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