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Integrate the following functions 1/sqrt...

Integrate the following functions `1/sqrt(8+3x-x^2)`

Text Solution

Verified by Experts

`8+3x-x^2 = 8-(x^2-3x)`
`=8-(x^2-3x+9/4-9/4)`
=`(41)/4 -(x_3/2)^2`
therefore `int 1/sqrt(8+3x-x^2)dx`
=`int 1/sqrt((41)/4-(x-3/2)^2 dx`
=`sin^-1(x-(3/2)/(sqrt41)/2)+c`
=`sin^-1((2x-3)/sqrt(41))+c`
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