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Category: Integration

Question-12635

Question Number 12635 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/Apr/17 Answered by mrW1 last updated on 27/Apr/17 $${x}^{\mathrm{2}} −\mathrm{2}{x}\mathrm{tan}\:\varphi−\mathrm{1} \\ $$$$={x}^{\mathrm{2}} −\mathrm{2}{x}\mathrm{tan}\:\varphi+\mathrm{tan}^{\mathrm{2}} \:\varphi−\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\varphi \\ $$$$=\left({x}−\mathrm{tan}\:\varphi\right)^{\mathrm{2}}…

1-3-sin-sin-2-d-

Question Number 78163 by TawaTawa last updated on 14/Jan/20 $$\int\:\sqrt{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{sin}\left(\theta\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\theta\right)}\:\:\mathrm{d}\theta \\ $$ Commented by MJS last updated on 15/Jan/20 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this} \\ $$ Commented by…

0-e-2arctg-t-2-dt-

Question Number 143622 by ArielVyny last updated on 16/Jun/21 $$\int_{\mathrm{0}} ^{\propto} {e}^{\mathrm{2}{arctg}\left({t}^{\mathrm{2}} \right)} {dt} \\ $$ Answered by TheHoneyCat last updated on 17/Jun/21 $$\mathrm{arctan}\left({t}\right)\underset{{t}\rightarrow+\infty} {\rightarrow}\frac{\pi}{\mathrm{2}}>\mathrm{0}…