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Category: Integration

Question-17180

Question Number 17180 by shankarnstephen last updated on 02/Jul/17 Commented by prakash jain last updated on 02/Jul/17 $$\int\frac{\mathrm{sin}\:{x}\centerdot{e}^{\mathrm{cos}\:{x}} −\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right){e}^{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}} }{{e}^{\mathrm{2sin}\:{x}} −\mathrm{2}{e}^{\mathrm{sin}\:{x}} +\mathrm{1}}{dx} \\ $$ Terms…

2dx-3x-5x-2-6-

Question Number 82700 by jagoll last updated on 23/Feb/20 $$\int\:\frac{\mathrm{2}{dx}}{\mathrm{3}{x}\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}}}\:? \\ $$ Commented by john santu last updated on 23/Feb/20 $$\int\:\frac{{d}\left({x}^{\mathrm{2}} \right)}{\mathrm{3}{x}^{\mathrm{2}} \:\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}}}\:,\:{let}\:{x}^{\mathrm{2}}…

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

Question Number 17086 by Joel577 last updated on 30/Jun/17 $$\underset{−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by Joel577 last updated on 30/Jun/17 $$\mathrm{How}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{like}\:\mathrm{this}? \\ $$$$\mathrm{Because}\:\mathrm{when}\:\mathrm{I}\:\mathrm{graph}\:\mathrm{the}\:\mathrm{function},…

sin-101x-sinx-99-dx-

Question Number 82617 by necxxx last updated on 23/Feb/20 $$\int\mathrm{sin}\:\left(\mathrm{101}{x}\right)\left({sinx}\right)^{\mathrm{99}} {dx} \\ $$ Answered by TANMAY PANACEA last updated on 23/Feb/20 $$\int{sin}\left({n}+\mathrm{1}\right){xsin}^{{n}−\mathrm{1}} {xdx}\:\:\:\:{n}=\mathrm{100} \\ $$$$\int\left({sinnxcosx}+{cosnxsinx}\right){sin}^{{n}−\mathrm{1}}…

cos-5x-cos-4x-dx-1-2cos-3x-

Question Number 82604 by jagoll last updated on 23/Feb/20 $$\int\:\frac{\mathrm{cos}\:\left(\mathrm{5}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}\right)\:{dx}}{\mathrm{1}−\mathrm{2cos}\:\left(\mathrm{3}{x}\right)}\:=\: \\ $$ Answered by john santu last updated on 23/Feb/20 $$\int\:\:\frac{\left\{\mathrm{cos}\:\left(\mathrm{5}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}\right)\right\}\mathrm{sin}\:\left(\mathrm{3}{x}\right)}{\mathrm{sin}\:\left(\mathrm{3}{x}\right)−\mathrm{sin}\:\left(\mathrm{6}{x}\right)}\:{dx} \\ $$$$=\mathrm{2}\int\:\frac{\left\{\mathrm{cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\right\}\mathrm{sin}\:\left(\mathrm{3}{x}\right)}{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{sin}\:\left(−\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}\:{dx} \\ $$$$=\:−\:\int\:\frac{\mathrm{sin}\:\left(\mathrm{3}{x}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{sin}\:\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}\:{dx}\:…

ln-sin-x-dx-

Question Number 148128 by puissant last updated on 25/Jul/21 $$\int\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{x}\right)\right)\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 25/Jul/21 $$\mathrm{Pas}\:\mathrm{de}\:\mathrm{formule}\:\mathrm{explicite}\:\mathrm{pour}\:\mathrm{ce}\:\mathrm{genre} \\ $$$$\mathrm{d}'\mathrm{integrales}\:\mathrm{mais}\:\mathrm{on}\:\mathrm{peut}\:\mathrm{quand}\:\mathrm{meme} \\ $$$$\mathrm{calculer}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{sur}\:\mathrm{un}\:\mathrm{intervalle}\:\mathrm{bien} \\…