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Category: Integration

Evaluate-tanx-cotx-tanx-cotx-sec-2-x-dx-

Question Number 14394 by tawa tawa last updated on 31/May/17 $$\mathrm{Evaluate}\:\:\:\int\:\left(\frac{\mathrm{tanx}\:−\:\mathrm{cotx}}{\mathrm{tanx}\:+\:\mathrm{cotx}}\:\mathrm{sec}^{\mathrm{2}} \mathrm{x}\right)\:\mathrm{dx} \\ $$ Answered by RasheedSindhi last updated on 31/May/17 $$\mathrm{Evaluate}\:\:\:\int\:\left(\frac{\mathrm{tanx}\:−\:\mathrm{cotx}}{\mathrm{tanx}\:+\:\mathrm{cotx}}\:\mathrm{sec}^{\mathrm{2}} \mathrm{x}\right)\:\mathrm{dx} \\ $$$$\:\int\:\left(\frac{\frac{\mathrm{sinx}}{\mathrm{cosx}}\:−\:\frac{\mathrm{cosx}}{\mathrm{sinx}}}{\frac{\mathrm{sinx}}{\mathrm{cosx}}\:+\:\frac{\mathrm{cosx}}{\mathrm{sinx}}}\:\mathrm{sec}^{\mathrm{2}}…

sin-x-2-2-dx-

Question Number 145456 by math55 last updated on 05/Jul/21 $$\int\boldsymbol{{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{2}\right)\boldsymbol{{dx}} \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\mathrm{F}\left({x}\right)\:=\:\int\mathrm{sin}\left({x}^{\mathrm{2}} +\mathrm{2}\right){dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\int\left(\mathrm{sin}\left({x}^{\mathrm{2}} \right)\mathrm{cos}\left(\mathrm{2}\right)+\mathrm{cos}\left({x}^{\mathrm{2}}…

For-witch-value-of-the-integral-I-0-1-1-2x-2-1-x-dx-converge-and-in-this-case-calculate-

Question Number 79869 by Henri Boucatchou last updated on 28/Jan/20 $${For}\:\:{witch}\:\:{value}\:\:{of}\:\:\alpha\:\:{the}\:\:{integral} \\ $$$$\:\:{I}=\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }}−\frac{\alpha}{\mathrm{1}+{x}}\right){dx}\:\:{converge}; \\ $$$$\:\:{and}\:\:{in}\:\:{this}\:\:{case}\:\:{calculate}\:\:\alpha \\ $$ Commented by mathmax by abdo…

0-pi-2-1-cos-2x-sin-2x-ln-sec-x-1-3-dx-

Question Number 145385 by mnjuly1970 last updated on 04/Jul/21 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}+\mathrm{cos}\:\left(\mathrm{2x}\right)}{\mathrm{sin}\:\left(\mathrm{2x}\:\right)}.\:\mathrm{ln}\sqrt[{\mathrm{3}}]{\mathrm{sec}\:\left(\mathrm{x}\right)}\:\mathrm{dx}=? \\ $$ Answered by mindispower last updated on 04/Jul/21 $${cos}\left(\mathrm{2}{x}\right)=\mathrm{2}{cos}^{\mathrm{2}} \left({x}\right)−\mathrm{1} \\ $$$$\Leftrightarrow−\frac{\mathrm{1}}{\mathrm{3}}\int_{\mathrm{0}}…