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Question
Find :
`∫(log x)^2 dx`
Solution
`∫(log x)^2 dx`
let `u = (logx)^2 , "v" = 1`
`∫u."v" dx = u∫"v"dx - ∫[(du)/dx∫"v"dx]dx`
`therefore ∫ (log x)^2 . 1dx = (log x)^2 ∫1dx - ∫[2log x xx 1/x xx xdx]`
= `x(log|x|^2) - 2∫log x dx`
`x(log x)^2 - 2(x log|x| - x) + C`
= `x(log|x|)^2 - 2x log|x| + 2x + C` .
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