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if i=∫2/x (x lnx ) (ln x) 3 dx = Ax lnx (lnx)^2- B x^ ln x +C, then A/B is equal to :

if i=∫2/x (xlnx) (ln x)3 dx = Axlnx(lnx)^2- B x^ln x+C, then A/B is equal to :

Grade:12th pass

1 Answers

Aditya Gupta
2086 Points
4 years ago
hello jahnvi, this is a very ez ques.
simply put y= lnx so that x= e^y and dx= xdy
so,  i=∫2/x (xlnx) (ln x)3 dx =  i=∫2e^(y^2)*y^3 dy
now 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+C
so A= B= 1
or A/B = 1
kindly approve :))

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