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.