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Question Number 96784 by 175 last updated on 04/Jun/20

Answered by Sourav mridha last updated on 04/Jun/20

$$=\int \frac{2+{\mathit{x}}^2+\mathit{x}}{{\mathit{x}}^2\sqrt{{\mathit{x}}^2+\mathit{x}+1}}\mathit{d}\mathit{x}+\frac{2}{\mathit{x}}$$$$=\int \frac{\mathit{d}(\mathit{x}+\frac{1}{2})}{\sqrt{{(\mathit{x}+\frac{1}{2})}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2}}+\frac{2}{\mathit{x}}$$$$-2\int \mathit{d}\left[\frac{\sqrt{{\mathit{x}}^2+\mathit{x}+1}}{\mathit{x}}\right]+\mathit{c}$$$$=\mathit{l}\mathit{n}[(\mathit{x}+\frac{1}{2})+\sqrt{{\mathit{x}}^2+\mathit{x}+1}]$$$$-2.\frac{\sqrt{{\mathit{x}}^2+\mathit{x}+1}}{\mathit{x}}+\frac{2}{\mathit{x}}+\mathit{c}$$

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