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Category: Integration

cos-6-x-dx-

Question Number 7898 by tawakalitu last updated on 23/Sep/16 $$\int{cos}^{\mathrm{6}} {x}\:\:{dx} \\ $$ Commented by sandy_suhendra last updated on 24/Sep/16 $${cos}^{\mathrm{6}} {x}\:=\:\left({cos}^{\mathrm{2}} {x}\right)^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}{cos}\mathrm{2}{x}\right)^{\mathrm{3}}…

Solve-cos-1-x-1-x-2-1-log-e-2-sin-2x-1-x-2-pi-dx-Evaluate-pi-2-pi-2-sin-2-xcos-2-x-cosx-sinx-dx-

Question Number 73429 by Henri Boucatchou last updated on 12/Nov/19 $$\:\:\:{Solve}\::\:\int\frac{\left[{cos}^{−\mathrm{1}} {x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right]^{−\mathrm{1}} }{{log}_{{e}} \left[\mathrm{2}+\frac{{sin}\left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{\pi}\right]}{dx} \\ $$$$\:\:{Evaluate}\:\:\int_{−\pi/\mathrm{2}} ^{\:\pi/\mathrm{2}} {sin}^{\mathrm{2}} {xcos}^{\mathrm{2}} {x}\left({cosx}+{sinx}\right){dx} \\ $$ Commented…

Evaluate-1-2-2-4-x-2-4-x-2-3-x-dydx-after-changing-the-integral-to-polar-form-2-0-4-0-4-x-0-4-y-2-4-dzdydx-

Question Number 73428 by Learner-123 last updated on 12/Nov/19 $${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\int_{−\mathrm{2}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} ^{\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} \:\left(\mathrm{3}−{x}\right){dydx}\:. \\ $$$$\left({after}\:{changing}\:{the}\:{integral}\:{to}\:{polar}\:{form}\right). \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\mathrm{4}}…

x-8-x-2-4x-16-dx-

Question Number 7872 by tawakalitu last updated on 22/Sep/16 $$\int\frac{{x}\:−\:\mathrm{8}}{{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:+\:\mathrm{16}}\:{dx} \\ $$ Commented by prakash jain last updated on 23/Sep/16 $$\frac{{x}−\mathrm{8}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{16}}=\frac{{x}−\mathrm{8}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{4}+\mathrm{12}} \\…