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intdx/((2x+5)sqrt(x+2)) |
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Answer» Solution :`intdx/((2x+5)sqrt(x+2))` [PUT x+2=t^2` dx=2tdt] =`int(2tdt)/([2(t^2-2)+5].t)=int(2dt)/(2t^2+1)` =`intdt/(t^2+(1/sqrt2)^2)=sqrt2tan^-1(sqrt2t)+C` =`sqrt2tan^-1(sqrt(2x+4))+C` |
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