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प्रश्न
Integrate the following with respect to x.
`("a"^x - "e"^(xlog"b"))/("e"^(x log "a") "b"^x)`
उत्तर
`int ("a"^x - "e"^(xlog"b"))/("e"^(x log "a") "b"^x) "d"x = int ("a"^x - "e"^(log("b")^x))/("e"^(log"a"^x) ("b")^x) "d"x`
= `int ("a"^x - "b"^x)/("a"^x"b"^x) "d"x`
= `int ("a"^x/("a"^x"b"^x) - "b"^x/("a"^x"b"^x)) "d"x`
= `int (1/"b"^x - 1/"a"^x) "d"x`
= `int ("b"^-x - "a"^-x) "d"x`
= `"b"^-x/((-1) log |"b"|) - "a"^-x/((-1) log|"a"|) + "c"`
= `"a"^-x/(log|"a"|) - "b"^-x/(log|"b"|) + "c"`
= `1/("a"^x log|"a"|) - 1/("b"^x log|"b"|)+ "c"`
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