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Q.

∫(9tan5x+7tan3x)(1+tan2x)dx(tan3x+tanx)12 =…

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a

2(tanx)52+c

b

2(tanx)72+c

c

2(tanx)72|secx|+c

d

None

answer is C.

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Detailed Solution

t=tanx,dt=sec2x dt ∫(9t5+7t3)dt(t3+t)1/2 ∫9t8+7t6(t9+t7)1/2dt             y=t9+t7 ⇒∫dyy⇒2y+c
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∫(9tan5x+7tan3x)(1+tan2x)dx(tan3x+tanx)12 =…