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Question
Find `int (2^(x + 1) - 5^(x - 1))/(10^x) dx`
Sum
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Solution
`int (2^(x + 1) - 5^(x - 1))/(10^x) dx = int (2^(x + 1) - 5^(x - 1))/(2^x.5^x) dx`
= `int (2^(x + 1)/(2^x.5^x) - 5^(x - 1)/(2^x.5^x)) dx`
= `int 2/5^x dx - int 1/(5.2^x) dx`
= `2 int 5^(-x) dx - 1/5 int 2^(-x) dx`
= `2 xx (-5^(-x))/(log 5) - 1/5 xx (-2^(-x))/(log 2)`
= `1/(5.2^x log 2) - 2/(5^x log 5)`
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