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Category: Integration

0-pi-12-sec-4-5sec-5-sin-2-sec-2-125tan-3-25tan-2-5tan-1-d-

Question Number 220184 by MathematicalUser2357 last updated on 07/May/25 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{12}}} \sqrt{\frac{\mathrm{sec}^{\mathrm{4}} \alpha+\mathrm{5sec}^{\mathrm{5}} \alpha\mathrm{sin}\:\alpha}{\left(\mathrm{2}−\mathrm{sec}^{\mathrm{2}} \alpha\right)\left(\mathrm{125tan}^{\mathrm{3}} \alpha+\mathrm{25tan}^{\mathrm{2}} \alpha+\mathrm{5tan}\:\alpha+\mathrm{1}\right)}}{d}\alpha \\ $$ Answered by MathematicalUser2357 last updated on…

R-R-I-x-2-ln-1-x-2-x-4-1-e-x-2-cos-x-dx-

Question Number 220065 by Nicholas666 last updated on 04/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\alpha\in\mathbb{R}\:\:\:;\:\:\:\:\omega\in\mathbb{R}^{+} \\ $$$$\:\:\:\:\:{I}\left(\alpha\right)\:=\:\int_{−\infty} ^{\:\infty} \:\frac{{x}^{\mathrm{2}} \:\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\alpha} }\:{e}^{−{x}^{\mathrm{2}} } \:\mathrm{cos}\left(\omega{x}\right)\:{dx} \\ $$$$ \\…

1-x-8-1-dx-

Question Number 220037 by Nicholas666 last updated on 04/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{8}} \:+\:\mathrm{1}}}\:{dx} \\ $$$$ \\ $$ Answered by MrGaster last updated on 04/May/25 $$\int\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{8}}…