Integral of (√3/x+2/x²-3/x³)dx?

1 Answer
maganbhai P.
Mar 5, 2018

#=sqrt3*lnx-2/x+3/(2x^2)+C#.

Explanation:

#color(red)((1)intx^ndx=(x^(n+1))/(n+1)+c)#
#color(red)((2)int1/xdx=lnx+c)#
#I=int(sqrt3/x+2/x^2-3/x^3)dx#, Using (1) and (2) we get,#I=sqrt3int1/xdx+2intx^-2dx-3intx^-3dx#
#=sqrt3*lnx+2(x^(-2+1)/(-2+1))-3((x^(-3+1))/(-3+1))+C#
#=sqrt3*lnx+2(x^-1/(-1))-3(x^(-2)/(-2))+C#
#=sqrt3*lnx-2/x+3/(2x^2)+C#.

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