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Evaluate int(x^(6)+x^(4)+x^(2))sqrt(2x^(...

Evaluate `int(x^(6)+x^(4)+x^(2))sqrt(2x^(4)+3x^(2)+6)dx`.

Text Solution

Verified by Experts

`I=int(x^(6)+x^(4)+x^(2))sqrt(2x^(4)+3x^(2)+6)`
`=int(x^(5)+x^(3)+x)sqrt(2x^(6)+3x^(4)+6x^(2))dx`
Let `2x^(6)+3x^(4)+6x^(2)=r^(2)`
` :. 12(x^(5)+x^(3)+x)dx=2t dt`
` :. I=(1)/(12)int2t^(2)dt=(1)/(18)(2x^(6)+3x^(4)+6x^(2))^(3//2)+c`
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