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Question

The inegral 3x13+2x11(2x4+3x2+1)4dx is equal to :
(where C is a 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
I=3x13+2x11(2x4+3x2+1)4 dx

=3x13+2x11x16(2+3x2+1x4)4 dx

=(3x3+2x5)(2+3x2+1x4)4 dx

Let 2+3x2+1x4=t
(6x3+4x5)dx=dt
(3x3+2x5)dx=12 dt

I=121t4 dt
=16t3+C
=x126(2x4+3x2+1)3+C

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