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Ed∫ex(cosx-sinxsin2x)dx = ______.

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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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