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Please solve the integration of sinx/sqt( sin^2 x +2cos x +3)

Please solve the integration of sinx/sqt( sin^2 x +2cos x +3)

Grade:12th pass

1 Answers

Aditya Gupta
2080 Points
2 years ago
hello mamta, the above question cn be solved by the following substitution:
put y=cosx and write sin^2x in the numerator as 1 – cos^2x
so the integration reduces to
– ∫dy/sqrt(1-y^2+2y+3)
= – ∫dy/sqrt(4-y^2+2y)
= – ∫dy/sqrt(5 – (y – 1)^2)
now put y-1=z
so we get
= – ∫dz/sqrt(5 – z^2)
you can easily find the above integral (using standard integration of 1/sqrt(a^2 – x^2) is arcsin(x/a))
 

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