∫$$x6+x4+x22x4+3x2+6dx$$

Correct option is 11182x6+3x4+6x23/2+C

Questions

$\int (x^{6} + x^{4} + x^{2}) \sqrt{2 x^{4} + 3 x^{2} + 6} d x$

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1182x6+3x4+6x23/2+C

1122x6+3x4+6x23/2+C

1182x6+3x4+6x22/3+C

1122x6+3x4+6x22/3+C

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detailed solution

Correct option is A

I=∫x6+x4+x22x4+3x2+6=∫x5+x3+x2x6+3x4+6x2dx Let 2x6+3x4+6x2=t2∴12x5+x3+xdx=2tdt∴I=112∫2t2dt=1182x6+3x4+6x23/2+c

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∫x6+x4+x22x4+3x2+6dx

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$\int (x^{6} + x^{4} + x^{2}) \sqrt{2 x^{4} + 3 x^{2} + 6} d x$