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Question

The value of 3x13+2x11(2x4+3x2+1)4dx is equal to
(where C is constant of integration )

A
x46(2x4+3x2+1)3+C
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B
x126(2x4+3x2+1)3+C
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C
x4(2x4+3x2+1)3+C
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D
x12(2x4+3x2+1)3+C
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Solution

The correct option is B x126(2x4+3x2+1)3+C
Let I=3x13+2x11(2x4+3x2+1)4dx
I=3x13+2x11x16(2+3x2+1x4)4dx
I=3x3+2x5(2+3x2+1x4)4dx
Put 2+3x2+1x4=t
2(3x3+2x5)dx=dt
I=12dtt4
I=16t3+C
I=16(2+3x2+1x4)3+C
I=x126(2x4+3x2+1)3+C

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