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Question Number 66971 by Cmr 237 last updated on 21/Aug/19

$$\int \frac{\mathrm{dx}}{\mathrm{x}\sqrt{{\mathrm{x}}^2+\mathrm{x}+1}}=?$$$$\mathbf{p}\mathfrak{l}\mathrm{ease}\mathrm{help}$$

Commented by MJS last updated on 21/Aug/19

$$\int \frac{dx}{x\sqrt{x^2+x+1}}=$$$$[t=\frac{1}{x}\to dx=-x^{2}dt]$$$$=-\int \frac{dt}{\sqrt{t^2+t+1}}=$$$$[u=2t+1\to dt=\frac{du}{2}]$$$$=-\int \frac{du}{\sqrt{u^2+3}}$$$$\mathrm{now}\mathrm{it}\mathrm{should}\mathrm{be}\mathrm{easy}$$

Commented by Cmr 237 last updated on 21/Aug/19

$$\mathfrak{t}\mathrm{hank}\mathrm{sir}$$

Commented by mathmax by abdo last updated on 23/Aug/19

$$thisintegralissolvedseetheQ66938$$

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