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if i=∫2/x (xlnx) (ln x)3 dx = Axlnx(lnx)^2- B x^ln x+C, then A/B is equal to :
hello jahnvi, this is a very ez ques.simply put y= lnx so that x= e^y and dx= xdyso, i=∫2/x (xlnx) (ln x)3 dx = i=∫2e^(y^2)*y^3 dynow put y^2= t so 2ydy= dt so i = ∫t*e^t dt = e^t*(t – 1) + C (integration by parts)= e^(y^2)*(y^2 – 1) + C= x^lnx*(ln^2x – 1) + C= xlnx(lnx)^2 – x^ln x+Cso A= B= 1or A/B = 1kindly approve :))
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