Menu Close

Category: Integration

Question-126529

Question Number 126529 by Study last updated on 21/Dec/20 Commented by Olaf last updated on 22/Dec/20 $$\mathrm{Why}\:{x}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}} \:\mathrm{is}\:\mathrm{not}\:{e}^{\mathrm{ln}\left[{x}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}} \right]} \:=\:{e}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}\mathrm{ln}{x}} \:=\:{e}\:\mathrm{sir}\:? \\ $$$$\mathrm{Why}\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{not}\:{e}.{x}+\mathrm{C}\:? \\ $$…

dx-sin-5-x-cos-7-x-

Question Number 126502 by benjo_mathlover last updated on 21/Dec/20 $$\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{5}} {x}\:\mathrm{cos}\:^{\mathrm{7}} {x}}}\:? \\ $$ Answered by MJS_new last updated on 21/Dec/20 $$\int\frac{{dx}}{\:\sqrt{\mathrm{sin}^{\mathrm{5}} \:{x}\:\mathrm{cos}^{\mathrm{7}} \:{x}}}= \\…