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प्रश्न
Integrate the following with respect to x.
`"e"^x/("e"^(2x) - 9)`
उत्तर
`int ("e"^x "d"x)/("e"^(2x) - 9) = int ("e"^x "d"x)/(("e"^x)^2 - 3^2)`
Let ex = t
Then ex dx = dt
= `int "dt"/("t"^2 - 3^2)`
= `1/(2(3)) log|("t" - 3)/("t" + 3)| +"c"`
= `1/6 log |("e"^x - 3)/("e"^x + 3)| + "c"`
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