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Category: Integration

Question-86407

Question Number 86407 by Power last updated on 28/Mar/20 Commented by mathmax by abdo last updated on 28/Mar/20 $$\left.{A}\:=\int\:\sqrt{\left({x}−{a}\right)\left({b}−{x}\right.}\right){dx}\:\Rightarrow{A}\:=\int\sqrt{{x}−{a}}\sqrt{{b}−{x}}{dx}\:{chsngement} \\ $$$$\sqrt{{x}−{a}}={t}\:{give}\:{x}−{a}\:={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${A}\:=\int\:\:{t}\sqrt{{b}−\left({a}+{t}^{\mathrm{2}} \right)}\left(\mathrm{2}{t}\right){dt}\:=\mathrm{2}\:\int\:{t}^{\mathrm{2}}…

Question-86405

Question Number 86405 by Power last updated on 28/Mar/20 Commented by MJS last updated on 28/Mar/20 $$\mathrm{sin}^{\mathrm{2}} \:\mathrm{3}{x}\:\mathrm{sin}^{\mathrm{3}} \:\mathrm{2}{x}\:= \\ $$$$=\frac{\mathrm{1}}{\mathrm{16}}\left(\mathrm{sin}\:\mathrm{12}{x}\:−\mathrm{3sin}\:\mathrm{8}{x}\:−\mathrm{2sin}\:\mathrm{6}{x}\:+\mathrm{3sin}\:\mathrm{4}{x}\:+\mathrm{6sin}\:\mathrm{2}{x}\right) \\ $$$$\mathrm{now}\:\mathrm{it}'\mathrm{s}\:\mathrm{super}\:\mathrm{easy} \\ $$…

dx-sin-2-x-tan-2-x-dx-

Question Number 86397 by M±th+et£s last updated on 28/Mar/20 $$\int\frac{{dx}}{{sin}^{\mathrm{2}} \left({x}\right)+{tan}^{\mathrm{2}} \left({x}\right)}\:{dx} \\ $$ Commented by Prithwish Sen 1 last updated on 28/Mar/20 $$−\mathrm{cotx}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\mid\mathrm{tan}^{\mathrm{2}} \mathrm{x}+\frac{\mathrm{1}}{\mathrm{2}}\mid+\mathrm{C}…

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

Question Number 86328 by M±th+et£s last updated on 28/Mar/20 $$\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}\:{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 28/Mar/20 $$\int\frac{\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}}…