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Category: Integration

tan-x-sin-3-x-cos-x-dx-

Question Number 218375 by Nicholas666 last updated on 08/Apr/25 $$ \\ $$$$\:\:\int\frac{\sqrt{\boldsymbol{{tan}}\:\boldsymbol{{x}}}}{\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}\:\boldsymbol{{cos}}\:\boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$$$ \\ $$ Answered by Ghisom last updated on 08/Apr/25 $$\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{sin}^{\mathrm{3}}…

Question-217881

Question Number 217881 by OmoloyeMichael last updated on 23/Mar/25 Answered by vnm last updated on 23/Mar/25 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\left(\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} {x}}\right){dx}={I} \\ $$$${f}\left({x}\right)=\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} {x}}…

cos-sin-1-x-cos-1-sin-x-ln-ln-ln-1-x-x-dx-

Question Number 217755 by Tawa11 last updated on 20/Mar/25 $$\int\:\frac{\mathrm{cos}\left(\mathrm{sin}^{−\:\mathrm{1}} \mathrm{x}\right)\:+\:\mathrm{cos}^{−\:\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{1}\:+\:\sqrt{\mathrm{x}\:+\:\sqrt{\mathrm{x}}}\right)\right.\right.}\:\mathrm{dx} \\ $$ Commented by mr W last updated on 20/Mar/25 $${you}\:{can}\:{even}\:{make}\:{it}\:{more}\:{nice} \\ $$$${looking}…