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Category: Integration

1-tan-3-2x-sec-5-2x-dx-2-0-pi-3-tan-5-x-sec-6-x-dx-3-tan-6-ay-dy-

Question Number 38130 by gunawan last updated on 22/Jun/18 $$\mathrm{1}.\:\int\mathrm{tan}^{\mathrm{3}} \left(\mathrm{2}{x}\right)\mathrm{sec}^{\mathrm{5}} \left(\mathrm{2}{x}\right)\:{dx}\: \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \mathrm{tan}^{\mathrm{5}} \left({x}\right)\mathrm{sec}^{\mathrm{6}} \left({x}\right)\:{dx}\: \\ $$$$\mathrm{3}.\:\int\mathrm{tan}^{\mathrm{6}} \left({ay}\right)\:{dy}\: \\ $$ Answered by…

f-is-a-function-positive-and-C-1-1-find-f-2-f-1-f-dx-2-let-A-n-0-1-x-n-2-x-1-x-n-calculate-A-n-and-lim-n-A-n-

Question Number 38123 by maxmathsup by imad last updated on 22/Jun/18 $${f}\:{is}\:{a}\:{function}\:{positive}\:\:{and}\:{C}^{\mathrm{1}} \:\: \\ $$$$\left.\mathrm{1}\right)\:{find}\:\int\:\:\:\:\frac{{f}^{'} }{\mathrm{2}\sqrt{{f}}\sqrt{\mathrm{1}+{f}}}{dx} \\ $$$$\left.\mathrm{2}\right){let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{x}^{\frac{{n}}{\mathrm{2}}} }{{x}\sqrt{\mathrm{1}+{x}^{{n}} }} \\ $$$${calculate}\:{A}_{{n}}…

prove-that-dx-1-x-2-ln-x-1-x-2-c-2-find-dx-a-x-2-with-a-gt-0-

Question Number 38124 by maxmathsup by imad last updated on 22/Jun/18 $${prove}\:{that}\:\:\int\:\:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:={ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:+{c} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{{a}+{x}^{\mathrm{2}} }}\:{with}\:{a}>\mathrm{0} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…