HERE IS ANOTHER WAY dx/x-x^3 multiply and divide by x so we have xdx/x^2-x^4 and put x^2=t so dx=dt/2x and hence the expression reduces to 1/2[dt/t-t^2] = 1/2[dt/t(1-t)] = 1/2[dt/t+dt/1-t] = 1/2[lnt-ln(1-t)] =1/2[lnt/1-t]+c substitute t=x^2 and you get the required ans
Moderation Team
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