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प्रश्न
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
पर्याय
`tan(x"e"^x) + "c"`
`cot(x"e"^x) + "c"`
`-tan(x"e"^x) + "c"`
`-cot(x"e"^x) + "c"`
MCQ
रिकाम्या जागा भरा
उत्तर
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = `-cot(x"e"^x) + "c"`.
Explanation:
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x = int"e"^x (x + 1)"cosec"^2 (x"e"^x)"d"x`
Put xex = t
⇒ (x + 1)ex dx = dt
∴ `int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x = int "cosec"^2"t" "dt" = - cot "t" + "c"`
= `- cot (x"e"^x) + "c"`
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