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Question Number 87862 by Rio Michael last updated on 06/Apr/20

Evaluate    ∫_(−1) ^1 (1/(x−1)) dx

$$\mathrm{Evaluate}\:\:\:\:\overset{\mathrm{1}} {\int}_{−\mathrm{1}} \frac{\mathrm{1}}{{x}−\mathrm{1}}\:{dx}\: \\ $$

Commented by MJS last updated on 06/Apr/20

doesn′t exist  ∫(dx/(x−1))=ln ∣x−1∣ +C  but lim_(x→1)  ln ∣x−1∣ =−∞

$$\mathrm{doesn}'\mathrm{t}\:\mathrm{exist} \\ $$$$\int\frac{{dx}}{{x}−\mathrm{1}}=\mathrm{ln}\:\mid{x}−\mathrm{1}\mid\:+{C} \\ $$$$\mathrm{but}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{ln}\:\mid{x}−\mathrm{1}\mid\:=−\infty \\ $$

Commented by Rio Michael last updated on 06/Apr/20

so sir can we say the integral diverges?

$$\mathrm{so}\:\mathrm{sir}\:\mathrm{can}\:\mathrm{we}\:\mathrm{say}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{diverges}? \\ $$

Commented by MJS last updated on 07/Apr/20

yes

$$\mathrm{yes} \\ $$

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