Menu Close

Category: Integration

sin-2-x-cos-x-1-3sin-2-x-dx-I-can-t-solve-this-maybe-some-genius-can-WolframAlpha-gives-a-solution-but-I-need-the-path-

Question Number 222595 by Ghisom last updated on 01/Jul/25 $$\Omega=\int\:\frac{\mathrm{sin}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{cos}\:{x}}}{\mathrm{1}+\mathrm{3sin}^{\mathrm{2}} \:{x}}{dx} \\ $$$$\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{solve}\:\mathrm{this},\:\mathrm{maybe}\:\mathrm{some}\:\mathrm{genius}\:\mathrm{can}. \\ $$$$\mathrm{WolframAlpha}\:\mathrm{gives}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{but}\:\mathrm{I} \\ $$$$\mathrm{need}\:\mathrm{the}\:\mathrm{path}… \\ $$ Commented by MrGaster last updated…

Prove-0-1-K-2-36K-2-6K-K-2-36K-2-dk-k-1-k-2-2-3-pi-2-4-2-2-3-0-1-K-2-36K-2-6K-2-K-2-36K-2-dk-k-1-k-2-2-3-

Question Number 222567 by MrGaster last updated on 30/Jun/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\sqrt{{K}^{\mathrm{2}} +\mathrm{36}{K}'^{\mathrm{2}} }+\mathrm{6}{K}^{'} }{{K}^{\mathrm{2}} +\mathrm{36}{K}^{'\mathrm{2}} }\:}\frac{{dk}}{\:\sqrt{{k}}\left(\mathrm{1}−{k}^{\mathrm{2}} \right)^{\frac{\mathrm{2}}{\mathrm{3}}} }=\sqrt{\pi}\left(\sqrt{\mathrm{2}}−\sqrt{\frac{\mathrm{4}−\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}}}\right) \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\sqrt{{K}^{\mathrm{2}}…

very-very-crazy-problem-i-am-not-found-what-is-the-result-of-this-integral-1-z-z-h-z-2h-dz-

Question Number 222541 by Nicholas666 last updated on 29/Jun/25 $$ \\ $$$$\:\:\:\mathrm{very}\:\mathrm{very}\:\mathrm{crazy}\:\mathrm{problem},\:\:\mathrm{i}\:\mathrm{am}\:\mathrm{not}\:\mathrm{found} \\ $$$$\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{integral}; \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\:\sqrt{{z}}\:+\:\sqrt{{z}−{h}}\:+\:\sqrt{{z}−\mathrm{2}{h}}}\:{dz} \\ $$$$ \\ $$ Commented by Ghisom last updated…