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Category: Integration

dx-a-bx-2-b-ax-2-

Question Number 36538 by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 $$\int\frac{{dx}}{\left({a}+{bx}^{\mathrm{2}} \right)\sqrt{{b}−{ax}^{\mathrm{2}} \:}}\:\: \\ $$ Commented by abdo.msup.com last updated on 03/Jun/18 $${we}\:{have}\:{b}\:−{ax}^{\mathrm{2}} ={b}\left(\mathrm{1}−\left(\sqrt{\frac{{a}}{{b}}}\:{x}\right)^{\mathrm{2}} \:\:{if}\:\frac{{a}}{{b}}>\mathrm{0}\right. \\…

x-1-x-2-n-dx-

Question Number 36541 by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 $$\int\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\right)^{{n}} {dx} \\ $$ Commented by prof Abdo imad last updated on 03/Jun/18 $${let}\:{put}\:\:{A}_{{n}} =\:\int\:\left({x}\:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…

Question-36537

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…

sin-3x-cos-5x-cos-2x-dx-

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 $$\int\frac{{sin}\mathrm{3}{x}−{sin}\mathrm{7}{x}}{{cos}\mathrm{2}{xcos}\mathrm{5}{x}}+\frac{{sin}\mathrm{7}{x}}{{cos}\mathrm{2}{xcos}\mathrm{5}{x}}=\int−\mathrm{2}{tan}\mathrm{2}{xdx}+\int\frac{{sin}\mathrm{5}{xcos}\mathrm{2}{x}+{cos}\mathrm{5}{xsin}\mathrm{2}{x}}{{cos}\mathrm{2}{xcos}\mathrm{5}{x}}{dx} \\ $$$$\int−{tan}\mathrm{2}{xdx}+\int{tan}\mathrm{5}{xdx}=\frac{\mathrm{1}}{\mathrm{2}}{log}\left({cos}\mathrm{2}{x}\right)−\frac{\mathrm{1}}{\mathrm{5}}{log}\left({cos}\mathrm{5}{x}\right)+{Constant} \\ $$…

cos-7x-cos-8x-1-2cos-5x-dx-

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}}…

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

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} \\…