The partial integral of sin2x/(D^2+6) is :a) 1/2 sin2x b) 1/10 sin2x c) 1/3 sin2x d)None of these

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem does not specify if you need to partial integrate with respect to `x`  or `D` (if D is a variable and not a constant), hence,partial integrating with respect to D yields:

`int sin2x/(D^2+6) delD = sin 2x*int (del D)/(D^2 + 6)`

`int sin2x/(D^2+6) delD = 1/(sqrt6)sin 2x*arctan(D/sqrt6) + c`

If you partial integrate with respect to x yields:

`int sin2x/(D^2+6) delx = 1/(D^2+6) int sin 2x del x`

`int sin2x/(D^2+6) delx = -(cos2x)/(2(D^2+6)) + c`

Hence, partial integrating the given function `sin2x/(D^2+6)`  yields that none of the answers `a),b),c)`  are not similar with the answers obtained, hence, the answer is d) None of these.

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