1.

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

Answer»

Solution :`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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