Question Number 36537 by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 Commented by Rasheed.Sindhi last updated on 03/Jun/18 $$\mathrm{Who}'\mathrm{s}\:\mathrm{the}\:\mathrm{author}?\:\mathrm{And}\:\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{book}? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on…
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Question Number 102064 by bramlex last updated on 06/Jul/20 $$\int\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{cos}\:\mathrm{5x}.\:\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 06/Jul/20 $$\int\frac{{sin}\mathrm{3}{x}−{sin}\mathrm{7}{x}}{{cos}\mathrm{2}{xcos}\mathrm{5}{x}}+\frac{{sin}\mathrm{7}{x}}{{cos}\mathrm{2}{xcos}\mathrm{5}{x}}=\int−\mathrm{2}{tan}\mathrm{2}{xdx}+\int\frac{{sin}\mathrm{5}{xcos}\mathrm{2}{x}+{cos}\mathrm{5}{xsin}\mathrm{2}{x}}{{cos}\mathrm{2}{xcos}\mathrm{5}{x}}{dx} \\ $$$$\int−{tan}\mathrm{2}{xdx}+\int{tan}\mathrm{5}{xdx}=\frac{\mathrm{1}}{\mathrm{2}}{log}\left({cos}\mathrm{2}{x}\right)−\frac{\mathrm{1}}{\mathrm{5}}{log}\left({cos}\mathrm{5}{x}\right)+{Constant} \\ $$…
Question Number 167596 by cortano1 last updated on 20/Mar/22 $$\:\:\int\:\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$ Answered by MJS_new last updated on 20/Mar/22 $$\frac{\mathrm{cos}\:\mathrm{7}{x}\:−\mathrm{cos}\:\mathrm{8}{x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5}{x}}= \\ $$$$\:\:\:\:\:\left[{c}=\mathrm{cos}\:{x}\right] \\ $$$$=−\frac{\left({c}−\mathrm{1}\right)\left(\mathrm{2}{c}+\mathrm{1}\right)\left(\mathrm{4}{c}^{\mathrm{2}} +\mathrm{2}{c}−\mathrm{1}\right)\left(\mathrm{16}{c}^{\mathrm{4}}…
Question Number 102065 by bramlex last updated on 06/Jul/20 $$\int\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\left(\mathrm{1}−\mathrm{x}\right)\sqrt{\mathrm{x}}}\:? \\ $$ Answered by PRITHWISH SEN 2 last updated on 06/Jul/20 $$\int\frac{\mathrm{1}−\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}−\mathrm{x}\right)\sqrt{\mathrm{x}}}\:\mathrm{dx}=\int\frac{\mathrm{dx}}{\left(\mathrm{1}−\mathrm{x}\right)\sqrt{\mathrm{x}}}\:−\int\frac{\left(\mathrm{1}+\mathrm{x}\right)}{\:\sqrt{\mathrm{x}}}\mathrm{dx} \\…
Question Number 167598 by cortano1 last updated on 20/Mar/22 $$\:\:\:\:\:\:\int\:\frac{\mathrm{x}}{\mathrm{5x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{3}} −\mathrm{5x}−\mathrm{1}}\:\mathrm{dx}=? \\ $$ Answered by MJS_new last updated on 20/Mar/22 $$\int\frac{{x}}{\mathrm{5}{x}^{\mathrm{4}} −\mathrm{5}{x}+{x}^{\mathrm{3}} −\mathrm{1}}{dx}=\int\frac{{x}}{\left(\mathrm{5}{x}+\mathrm{1}\right)\left({x}^{\mathrm{3}} −\mathrm{1}\right)}{dx}=…
Question Number 102058 by Dwaipayan Shikari last updated on 06/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({logx}\right)}{{logx}}{dx} \\ $$ Answered by prakash jain last updated on 06/Jul/20 $${x}={e}^{{u}} \\…
Question Number 167586 by cortano1 last updated on 20/Mar/22 $$\:\:\:\:\:\:\:\:\lambda=\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\:=? \\ $$ Commented by MJS_new last updated on 20/Mar/22 $$\mathrm{1}^{\mathrm{st}} \:\mathrm{step}\:{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}} \\ $$$$\mathrm{2}^{\mathrm{nd}} \:\mathrm{step}\:{u}={t}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}…