Question

How do you evaluate `int_2^4 5^(2x) dx`?

Answer 1

`(25^5-25^2)/ln25`.

Explanation:

Let, `I=int_2^5 5^(2x)dx=int_2^5 (5^2)^xdx=int_2^5 25^xdx`.

Now, recall that, `inta^xdx=a^x/lna+C`.

Hence, `I=[25^x/ln25]_2^5=(25^5-25^2)/ln25`