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If int (x^9+x^6+x^3)(2x^6+3x^3+6)^(1/3) ...

If `int (x^9+x^6+x^3)(2x^6+3x^3+6)^(1/3) dx=1/a(2x^9+3x^6+6x^3)^(4/3)+c`, then 'a' is equal to:

Text Solution

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`I=int(x^9+x^6+x^3)(2x^9+3x^6+6x^3)^(1/3)/x^3dx`
`I=int(x^8+x^5+x^2)(2x^9+3x^6+6x^3)^(1/3)dx`
`2x^9+3x^6+6x^3=t`
`18x^8+18x^5+18x^2 dx=dt`
`(x^8+x^5+x^2)dx=dt/18`
`I=intt^(1/3)/18 dt`
`I=1/18*t^(4/3)/(4/3)`
`I=1/24(2x^9+3x^6+6x^3)^(4/3)+c`
...
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