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Application Of Integrals

Question
CBSEENMA12036192

integral fraction numerator dx over denominator cos space straight x space plus space square root of 3 space sin space straight x end fraction equals
  • 1 half space log space tan space open parentheses straight x over 2 plus straight pi over 12 close parentheses space plus straight C
  • 1 half space log space tan space open parentheses straight x over 2 minus straight pi over 12 close parentheses plus straight c
  • log space tan space open parentheses straight x over 2 minus straight pi over 12 close parentheses plus straight c
  • log space tan space open parentheses straight x over 2 plus straight pi over 12 close parentheses plus straight c

Solution

A.

1 half space log space tan space open parentheses straight x over 2 plus straight pi over 12 close parentheses space plus straight C integral fraction numerator dx over denominator cos space straight x space space plus space square root of 3 space sin space straight x end fraction
space equals space 1 half space integral sec space open parentheses straight x minus straight pi over 3 close parentheses dx
equals space 1 half space log space tan space open parentheses straight x over 2 minus straight pi over 6 plus straight pi over 4 close parentheses space plus straight C
space equals space 1 half space log space tan space open parentheses straight x over 2 plus straight pi over 12 close parentheses space plus straight C