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Category: Integration

sin-5-x-dx-cos-x-

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-97707

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}}…

Evaluate-0-1-1-16-9x-2-dx-

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-163212

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-163197

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}…