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Integrate the following functions (xcos^...

Integrate the following functions `(xcos^-1x)/sqrt(1-x^2)`

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`int (x cos^-1 x)/sqrt(1-x^2) dx`
=`1/2 int (-2x)/sqrt(1-x^2) cos^-1 x dx`
=`-1/2 [cos^-1 x xx 2 sqrt(1-x^2) - int -1/sqrt(1-x^2) 2 sqrt(1-x^2) dx]`
=`-1/2 [2sqrt(1-x^2) cos^-1 x+2 int dx]`
=`-1/2[2sqrt(1-x^2) cos^-1x +2x]+c`
=`-[sqrt(1-x^2) cos^-1 x+x]+c`
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