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Integrate the functions(x^3-1)^(1/3)x^5...

Integrate the functions`(x^3-1)^(1/3)x^5`

Text Solution

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Given,`(x^3-1)^(1/3)x^5`
Put `x^3−1=t`
∴`3x^2dx=dt`
⇒`∫(x^3-1)^(1/3)x^5dx=∫(x^3-1)^(1/3)x^3.x^2dx`
=`∫t^(1/3).​(t+1)dt/3​`
=`1/3∫(t^(4/3)​+t^(1/3)​)dt`
=`1/3[[t^(7/3)]/(7/3)+[t^(4/3)]/(4/3)]+C`
=`1/3​[3/7*t^(7/3)​+3/4*​t^(4/3)​]+C`
...
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