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int(4^(x+1)-7^(x-1))/(28^(x))dx is equal...

`int(4^(x+1)-7^(x-1))/(28^(x))dx` is equal to

A

`(1)/(7log_(e)4)4^(-x)-(4)/(log_(e)7)7^(-x)+C`

B

`(1)/(7log_(e)4)4^(-x)+(4)/(log_(e)7)7^(-x)+C`

C

`(4^(-x))/(log_(e)7)-(7^(-x))/(log_(e)4)+C`

D

`(4^(-x))/(log_(e)4)-(7^(-x))/(log_(e)7)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I=int{(4^(x+1))/(28^(x))-(7^(x-1))/(28^(x))}dx`
`=4int(1)/(7^(x))dx-(1)/(7)int(1)/(4^(x))dx`
`=-(4.7^(-x))/(log_(e)7)+(1)/(7log_(e)4)4^(-x)+C`
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