Q. ¡ò(15^x/3^x) dx

i know that the ¡ò(a^x) dx = a^x/lna +c
but i don't know how to solve this question.

thank you

Your expression came out with a weird symbol on my computer.

Is that supposed to be an integral sign?

Did you want
[integral] (15^x/3^x) dx ??

15^x/3^x = (15/3)^x = 5^x

since you don't have any upper or lower limits on the integral, you want the indefinite integral

[integral] 5^x dx = 5^x/ln5 + c

You were on the right track.

Thank you so much!!!

integration1-e integration 0-lnx y dy dx

To solve the integral ∫(15^x/3^x) dx, you can simplify the expression by rewriting it as (15/3)^x = 5^x.

Now we have ∫(5^x) dx.

To integrate 5^x, you can use a property of exponential functions. For any constant base "a", the integral of a^x with respect to x is given by a^x/ln(a) + C, where ln denotes the natural logarithm.

In this case, a = 5, so the integral becomes:

∫(5^x) dx = 5^x/ln(5) + C.

Therefore, the solution to the integral ∫(15^x/3^x) dx is:

∫(15^x/3^x) dx = 5^x/ln(5) + C.