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Q.

If ∫(1−tan⁡3x)2dx=12[tan⁡3x+log⁡f(x)]+C then f(x) is given by

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a

cos⁡3x

b

cos2⁡3x

c

sin2⁡3x

d

cos3⁡3x

answer is B.

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Detailed Solution

∫(1−tan⁡3x)2dx=∫1+tan2⁡3x−2tan⁡3xdx=∫sec2⁡3x−2tan⁡3xdx=tan⁡3x3−23log⁡|sec⁡3x|+C=13tan⁡3x+log⁡cos2⁡3x+C
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