How do you integrate #f(x)=5^x/2^x# using the quotient rule?

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Answer 1 · 2016-09-25T06:55:22

#intf(x)dx=5^x/(2^xln(5/2))+C.#

In the first instance, there is no Rule called Quotient Rule for

Integration !

However, the fun. #f(x)=5^x/2^x#, can easily be integrated, using the

following Standard Integral :-

#inta^xdx=a^x/lna+C, a in RR^+ -{1}, x in RR#.

Since, #5^x/2^x=(5/2)^x, we have,

#intf(x)dx=int(5/2)^xdx=(5/2)^x/ln(5/2)=5^x/(2^xln(5/2))+C.#