Q.

If ∫cos⁡xcos⁡2xcos⁡5xdx=A1sin⁡2x+A2sin⁡4x+A3sin⁡6x+A4sin⁡8x+Cthen

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a

A1=12,A2=14

b

A1=14,A2=18

c

A2=116,A3=18

d

A1=18, A4=132

answer is D.

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Detailed Solution

(cos⁡xcos⁡2x)cos⁡5x=12(cos⁡x+cos⁡3x)cos⁡5x=14[cos⁡4x+cos⁡6x]+14[cos⁡2x+cos⁡8x]=14cos⁡2x+14cos⁡4x+14cos⁡6x+14cos⁡8x∫cos⁡xcos⁡2xcos⁡5xdx=18sin⁡2x+116sin⁡4x+124sin⁡6x+132sin⁡x+C
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If ∫cos⁡xcos⁡2xcos⁡5xdx=A1sin⁡2x+A2sin⁡4x+A3sin⁡6x+A4sin⁡8x+Cthen