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Category: Integration

x-5-x-3-1-1-3-dx-

Question Number 11149 by suci last updated on 14/Mar/17 $$\int{x}^{\mathrm{5}} \:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}=…??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$\:\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{7}/\mathrm{3}} }{\mathrm{7}}−\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}}…

sin-3-1-2x-dx-

Question Number 11146 by suci last updated on 14/Mar/17 $$\int{sin}^{\mathrm{3}} \left(\mathrm{1}+\mathrm{2}{x}\right){dx}=….??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:−\frac{\mathrm{3}}{\mathrm{8}}\mathrm{cos}\:\left(\mathrm{2}{x}+\mathrm{1}\right)+\frac{\mathrm{1}}{\mathrm{24}}\mathrm{cos}\:\left(\mathrm{6}{x}+\mathrm{3}\right)+{C} \\ $$ Commented by…

Question-142191

Question Number 142191 by iloveisrael last updated on 27/May/21 Commented by Mathspace last updated on 27/May/21 $${why}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={i}+\frac{\mathrm{2}{i}}{\mathrm{1}+{e}^{{ix}} }\:? \\ $$$${and}\:{what}\:{is}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sin}\left({nx}\right)}{\mathrm{1}+{e}^{{ix}} }{dx} \\ $$$${all}\:{this}\:{need}\:{proof}……

6-dx-x-2-3x-2-7-4dx-x-2-2x-4-8-3-2xdx-x-2-64-9-3x-1-x-3-5x-2-6x-dx-10-4-3x-x-3-2x-dx-11-dx-x-3-2x-x-

Question Number 142149 by cesarL last updated on 27/May/21 $$\mathrm{6}.\:\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$$$\mathrm{7}.\:\int\frac{\mathrm{4}{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}} \\ $$$$\mathrm{8}.\:\int\frac{\mathrm{3}−\mathrm{2}{xdx}}{{x}^{\mathrm{2}} −\mathrm{64}} \\ $$$$\mathrm{9}.\:\int\frac{\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}{x}}{dx} \\ $$$$\mathrm{10}.\:\int\frac{\mathrm{4}−\mathrm{3}{x}}{{x}^{\mathrm{3}} −\mathrm{2}{x}}{dx} \\…

sec-3-x-dx-

Question Number 76615 by mhmd last updated on 28/Dec/19 $$\int{sec}^{\mathrm{3}} {x}\:{dx} \\ $$ Answered by $@ty@m123 last updated on 28/Dec/19 $$\int\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} {x}}.\mathrm{sec}\:^{\mathrm{2}} {xdx} \\ $$$$\int\sqrt{\mathrm{1}+{t}^{\mathrm{2}}…