Question Number 97759 by bobhans last updated on 09/Jun/20 $$\int\:\frac{\mathrm{sin}\:^{\mathrm{5}} \left({x}\right)\:{dx}}{\:\sqrt{\mathrm{cos}\:\left({x}\right)}}\:? \\ $$ Answered by bemath last updated on 09/Jun/20 $$\int\:\frac{\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\right)^{\mathrm{2}} \mathrm{sin}\:{x}\:{dx}}{\:\sqrt{\mathrm{cos}\:{x}}}\:= \\ $$$${set}\:\sqrt{\mathrm{cos}\:{x}}\:=\:{z}\:\Rightarrow\:−\mathrm{sin}\:{x}\:{dx}\:=\:\mathrm{2}{z}\:{dz}…
Question Number 32206 by Glorious Man last updated on 21/Mar/18 $$\mathrm{Find}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\underset{\mathrm{k}−\mathrm{1}} {\overset{\mathrm{k}} {\int}}\mathrm{x}^{−\mathrm{x}} \:\mathrm{dx}\right)\:. \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 97721 by Power last updated on 09/Jun/20 Commented by mr W last updated on 09/Jun/20 Commented by smridha last updated on 09/Jun/20 $${this}\:{is}\:{not}\:\boldsymbol{{the}}\:\boldsymbol{{solution}}!!!…
Question Number 97707 by Power last updated on 09/Jun/20 Answered by smridha last updated on 09/Jun/20 $$=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{e}}^{\boldsymbol{{ix}}} }{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }\boldsymbol{{dx}}\:+\frac{\mathrm{1}}{\mathrm{2}}\int_{+\infty} ^{−\infty} \frac{\boldsymbol{{e}}^{−\left(−\boldsymbol{{ix}}\right)} }{\left(−\boldsymbol{{x}}\right)^{\mathrm{2}}…
Question Number 97683 by Don08q last updated on 09/Jun/20 $$\:\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{16}\:+\:\mathrm{9}{x}^{\mathrm{2}} }}\:{dx} \\ $$ Commented by bemath last updated on 09/Jun/20 $$\mathrm{set}\:\mathrm{3x}\:=\:\mathrm{4tan}\:\mathrm{z}\:\Rightarrow\mathrm{3dx}=\mathrm{4sec}\:^{\mathrm{2}} \mathrm{zdz} \\…
Question Number 163212 by smallEinstein last updated on 04/Jan/22 Commented by mr W last updated on 05/Jan/22 $${what}\:{a}\:{pity},\:{Mr}\:{Einstein}!\:{i}\:{have}\:{asked} \\ $$$${you}\:{for}\:{more}\:{times}\:{to}\:{crop}\:{the}\:{image}\: \\ $$$${properly}\:{when}\:{you}\:{are}\:{posting}\:{it}. \\ $$$${but}\:{you}\:{ignored}\:{my}\:{suggestion}\:{and} \\…
Question Number 32139 by Cheyboy last updated on 20/Mar/18 $${F}\boldsymbol{{ind}}\:\boldsymbol{{the}} \\ $$$$\int\:\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Commented by mrW2 last updated on 20/Mar/18 $$\int\:\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\…
Question Number 97671 by I want to learn more last updated on 09/Jun/20 Commented by MJS last updated on 09/Jun/20 $${question}\:\mathrm{97624} \\ $$ Terms of…
Question Number 163197 by abdullahhhhh last updated on 04/Jan/22 Commented by cortano1 last updated on 05/Jan/22 $$\mathrm{cos}\:\mathrm{5}{x}=\mathrm{cos}\:^{\mathrm{5}} {x}−\mathrm{10sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:^{\mathrm{3}} {x}+\mathrm{5sin}\:^{\mathrm{4}} {x}\:\mathrm{cos}\:{x} \\ $$$$\mathrm{sin}\:\mathrm{4}{x}=\mathrm{4sin}\:{x}\:\mathrm{cos}\:^{\mathrm{3}} {x}−\mathrm{4sin}\:^{\mathrm{3}} {x}\:\mathrm{cos}\:{x}…
Question Number 97660 by bobhans last updated on 09/Jun/20 Commented by bemath last updated on 09/Jun/20 $$\mathrm{nice}\:\mathrm{question} \\ $$ Answered by bemath last updated on…