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Question Number 166263 by cortano1 last updated on 17/Feb/22

$${\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\frac{\mathrm{dx}}{\cos {}^2\mathrm{x}\sqrt{9+7\tan \mid \mathrm{x}\mid }}\mathrm{dx}=?$$

Answered by mathsmine last updated on 17/Feb/22

$$=2{\int }_0^{\frac{\pi }{4}}\frac{dx}{{cos}^2\left(x\right)\sqrt{9+7tg\left(x\right)}}$$$$=2{\int }_0^1\frac{du}{\sqrt{9+7u}}=\frac{4}{7}\left({\left[\sqrt{9+7u}\right]}_0^1\right)$$$$=\frac{4}{7}$$

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