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Integrate the following functions xsqrt(...

Integrate the following functions `xsqrt(x+2)`

Text Solution

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`xsqrt(x+2) = (x+2-2) sqrt(x+2)`
=`(x+2) sqrt(x+2)-2sqrt(x+2)`
=`(x+2)^(3/2) -2(x+2)^(1/2)`
therefore `int xsqrt(x+2) dx`
=`(x+2)^(3/2+1)/(3/2+1) -2 (x+2)^(1/2+1)/(1/2+1) +c`
=`2/5 (x+2)^(5/2) -4/3 (x=2)^(3/2) +c`
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