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Question Number 164854 by Zaynal last updated on 22/Jan/22

Evaluate the Integral; [∫_0 ^∞ ((x^2 − 1)/(1−x)) dx =??] ^({Z.A})

EvaluatetheIntegral;[∫0∞x2−11−xdx=??]{Z.A}

Answered by MJS_new last updated on 22/Jan/22

lim_(x→1) ((x^2 −1)/(1−x)) =−2 ⇒ ∫((x^2 −1)/(1−x))dx=−∫(x+1)dx ⇒ ∫_0 ^∞ ((x^2 −1)/(1−x))dx doesn′t converge

limx→1x2−11−x=−2⇒∫x2−11−xdx=−∫(x+1)dx⇒∫∞0x2−11−xdxdoesn′tconverge

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