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Q.

∫01x3(1+x2)3dx=

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a

18

b

14

c

112

d

116

answer is D.

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Detailed Solution

∫0π/4Tan3θ(Sec2θ)3×Sec2θ dθ       x=tanθ,dx=sec2dθ    =∫0π/4Tan3θSec4θdθ  =∫0π/4Sin3θ.Cosθ dθ  =(Sin4θ4)0π/4   1244=116
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