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Category: Integration

dx-x-4x-2-2x-1-

Question Number 91842 by jagoll last updated on 03/May/20 $$\int\:\frac{{dx}}{{x}\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}}\:? \\ $$ Commented by mathmax by abdo last updated on 03/May/20 $${I}\:=\int\:\:\frac{{dx}}{{x}\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}}\:\:{let}\:{solve}\:\mathrm{4}{x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{1}\:=\mathrm{0}\:\rightarrow…

cosec-x-dx-

Question Number 26270 by ibraheem160 last updated on 23/Dec/17 $$\int\sqrt{{cosec}\left({x}\right)}{dx} \\ $$ Commented by prakash jain last updated on 24/Dec/17 $$\mathrm{Please}\:\mathrm{provide}\:\mathrm{some}\:\mathrm{context}. \\ $$$$\mathrm{This}\:\mathrm{integral}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{expressed} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{elementry}\:\mathrm{functiin}.…

prove-that-k-0-k-n-cos-2-kx-n-1-2-sin-n-1-x-cos-nx-2-sinx-x-from-R-kpi-k-Z-then-find-the-value-of-integral-0-pi-sin-n-1-x-cos-nx-sinx-dx-

Question Number 26242 by abdo imad last updated on 22/Dec/17 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{k}={n}} \:\:{cos}^{\mathrm{2}} \left({kx}\right)=\:\frac{{n}+\mathrm{1}}{\mathrm{2}}\:\:+\:\frac{{sin}\left(\left({n}+\mathrm{1}\right){x}\right){cos}\left({nx}\right)}{\mathrm{2}\:{sinx}} \\ $$$${x}\:{from}\:{R}−\left\{\:{k}\pi.{k}\varepsilon{Z}\right\}{then}\:{find}\:{the}\:{value}\:{of}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\left(\left({n}+\mathrm{1}\right){x}\right){cos}\left({nx}\right)}{{sinx}}{dx} \\ $$$$ \\ $$ Commented…