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Category: Integration

x-2-cos-x-2-dx-

Question Number 141333 by cesarL last updated on 17/May/21 $$\int{x}^{\mathrm{2}} \mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right){dx} \\ $$ Answered by qaz last updated on 17/May/21 $$\int{x}^{\mathrm{2}} \mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx} \\ $$$$=\mathrm{2}{x}^{\mathrm{2}} \mathrm{sin}\:\frac{{x}}{\mathrm{2}}−\mathrm{4}\int{x}\mathrm{sin}\:\frac{{x}}{\mathrm{2}}{dx}…

a-a-sin-x-cos-x-dx-

Question Number 10241 by FilupSmith last updated on 31/Jan/17 $$\int_{{a}} ^{\:{a}+\delta} \frac{\mathrm{sin}\left({x}\right)}{\mathrm{cos}\left({x}+\delta\right)}{dx}\:=\:??? \\ $$ Commented by prakash jain last updated on 31/Jan/17 $$\frac{\mathrm{sin}\left({x}\right)}{\mathrm{cos}\left({x}+\delta\right)}=\frac{\mathrm{sin}\left({x}+\delta−\delta\right)}{\mathrm{cos}\left({x}+\delta\right)} \\ $$$$=\frac{\mathrm{sin}\:\left({x}+\delta\right)\mathrm{cos}\:\delta−\mathrm{cos}\:\left({x}+\delta\right)\mathrm{sin}\:\delta}{\mathrm{cos}\:\left({x}+\delta\right)}…

Question-75770

Question Number 75770 by Ajao yinka last updated on 16/Dec/19 Commented by ~blr237~ last updated on 17/Dec/19 $$\mathrm{A}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{x}} \sqrt{\mathrm{sinh2x}}}\:=\sqrt{\mathrm{2}}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{e}^{−\mathrm{x}} \mathrm{dx}}{\:\sqrt{\mathrm{e}^{\mathrm{2x}} −\mathrm{e}^{−\mathrm{2x}}…

Question-75750

Question Number 75750 by rajesh4661kumar@gmail.com last updated on 16/Dec/19 Commented by MJS last updated on 16/Dec/19 $$\mathrm{this}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{using}\:\mathrm{elementary} \\ $$$$\mathrm{calculus} \\ $$$$\mathrm{a}\:\mathrm{solution}\:\mathrm{was}\:\mathrm{posted}\:\mathrm{on}\:\mathrm{this}\:\mathrm{forum}\:\mathrm{some} \\ $$$$\mathrm{time}\:\mathrm{ago} \\ $$…