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Question Number 179853 by AKSHAYTHAKUR last updated on 03/Nov/22

$$\int \frac{\mathit{x}\mathit{d}\mathit{x}}{(\mathit{x}-1)(\mathit{x}-2)}$$

Commented by CElcedricjunior last updated on 04/Nov/22

$$\int \frac{\mathit{x}\mathit{d}\mathit{x}}{(\mathit{x}-1)(\mathit{x}-2)}=\int [\frac{1}{\mathit{x}-2}+\frac{1}{(\mathit{x}-1)(\mathit{x}-2)}]\mathit{d}\mathit{x}$$$$=ln\mid \mathit{x}-2\mid +\int [-\frac{1}{\mathit{x}-1}+\frac{1}{\mathit{x}-2}]\mathit{d}\mathit{x}$$$$=\mathit{l}\mathit{n}\mid \mathit{x}-2\mid -\mathit{l}\mathit{n}\mid \mathit{x}-1\mid +\mathit{l}\mathit{n}\mid \mathit{x}-1\mid$$$$=\mathit{l}\mathit{n}\mid \frac{{(\mathit{x}-2)}^2}{\mathit{x}-1}\mid +\mathit{c}\mathit{s}\mathit{t}\mathit{e}$$$$=>\int \frac{\mathit{x}\mathit{d}\mathit{x}}{(\mathit{x}-1)(\mathit{x}-2)}=\mathit{l}\mathit{n}\mid \frac{{(\mathit{x}-2)}^2}{\mathit{x}-1}\mid +\mathit{c}\mathit{s}\mathit{t}\mathit{e}$$$$..............lecelebrecedricjunior........$$

Commented by Frix last updated on 04/Nov/22

$$\ln a-\ln b=\ln \frac{a}{b}\ne \frac{\ln a}{\ln b}$$$$\mathrm{your}\mathrm{answer}\mathrm{is}\mathrm{wrong}$$

Answered by Frix last updated on 03/Nov/22

$$\int \frac{x}{(x-1)(x-2)}dx=\int (\frac{2}{x-2}-\frac{1}{x-1})dx=$$$$=2\ln \mid x-2\mid -\ln \mid x-1\mid +C$$

Commented by AKSHAYTHAKUR last updated on 09/Nov/22

$$thankyouser$$

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