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Question Number 43803 by vc526 last updated on 15/Sep/18

$$\mathrm{\infty }$$$$\int \frac{1}{x\mathrm{l}nx}dx=$$$$0$$

Answered by tanmay.chaudhury50@gmail.com last updated on 15/Sep/18

$$t=lnx$$$$dt=\frac{dx}{x}$$$${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{dt}{t}$$$$\underset{a\to -\mathrm{\infty }}{\lim }{\int }_a^{\mathrm{\infty }}\frac{dt}{t}$$$$=\underset{a\to -\mathrm{\infty }}{\lim }\mid lnt{\mid }_a^{\mathrm{\infty }}$$$$=\underset{a\to -\mathrm{\infty }}{\lim }\{ln\mathrm{\infty }-lna\}$$$$=\underset{a\to -\mathrm{\infty }}{\lim }\{\mathrm{\infty }-lna\}$$$$$$

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