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  1. #1
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    integrate

    integrate (square root t)/(1+ t^(1/3))
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  2. #2
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    Quote Originally Posted by twilightstr View Post
    integrate (square root t)/(1+ t^(1/3))
     <br />
 \int{\frac{\sqrt{x}}{1+x^{1/3}}}<br /> <br />
    Put
     <br />
x= t^6<br />
    dx=6t^5dt

     <br />
= \int{\frac{t^3 \times 6t^5}{1+t^2}}<br />

     <br />
=6 \int{\frac{t^8}{1+t^2}}<br />


    =6 \int{\frac{t^8+1-1}{1+t^2}}

     <br />
=6 \int{\frac{t^8-1}{1+t^2}} + 6 \int{\frac{1}{1+t^2}}<br /> <br />

     <br />
=6 \int{\frac{(t^4+1)(t^2+1)(t^2-1)}{1+t^2}} + 6 \int{\frac{1}{1+t^2}}<br />

     <br />
=6 \int{(t^4+1)\times (t^2-1)} + 6 \int{\frac{1}{1+t^2}}<br /> <br />

    Once again Go ahead
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