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Question
`int "e"^x ((cos x - sin x)/(sin^2x)) "d"x` = ______.
Options
ex cot x + c
– ex cot x + c
ex cosec x + c
– ex cosec x + c
MCQ
Fill in the Blanks
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Solution
`int "e"^x ((cos x - sin x)/(sin^2x)) "d"x` = – ex cosec x + c.
Explanation:
= `int "e"^x (cot x "cosec" x - "cosec" x) "d"x`
= `- int "e"^x (- cot x "cosec" x + "cosec" x) "d"x`
= `- "e"^x "cosec" x + "c"` .....`[because int "e"^x["f"(x) + "f'"(x)] "d"x = "e"^x"f"(x) + "c"]`
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Integrals of Trignometric Functions
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