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Category: Integration

Integrate-the-following-1-a-x-x-dx-2-dx-sin-x-3-2-cos-x-

Question Number 84234 by niroj last updated on 10/Mar/20 $$\:\:\boldsymbol{\mathrm{Integrate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}: \\ $$$$\:\:\:\mathrm{1}.\:\int\sqrt{\frac{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\:\:\mathrm{2}.\int\:\:\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\left(\mathrm{3}+\mathrm{2}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\right)} \\ $$$$\: \\ $$ Commented by mathmax by abdo last updated…

Question-149739

Question Number 149739 by iloveisrael last updated on 07/Aug/21 Answered by Olaf_Thorendsen last updated on 07/Aug/21 $$\lambda\:=\:\int_{\mathrm{0}} ^{\pi} {x}\mathrm{sin}^{\mathrm{9}} {x}\:{dx}\:\:\:\left(\mathrm{1}\right) \\ $$$$\lambda\:=\:\int_{\pi} ^{\mathrm{0}} \left(\pi−{u}\right)\mathrm{sin}^{\mathrm{9}} \left(\pi−{u}\right)\:\left(−{du}\right)…

dx-x-x-4-1-

Question Number 18650 by thukada last updated on 26/Jul/17 $$\int{dx}/{x}\sqrt{{x}^{\mathrm{4}} −\mathrm{1}} \\ $$ Answered by sma3l2996 last updated on 26/Jul/17 $${A}=\int\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}} \\ $$$${let}\:\:{t}=\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}\Rightarrow{dt}=\frac{\mathrm{2}{x}^{\mathrm{3}}…

dx-x-3-4-x-3-1-3-

Question Number 84170 by jagoll last updated on 10/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{4}−\mathrm{x}^{\mathrm{3}} }}\:?\: \\ $$ Answered by john santu last updated on 10/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:\sqrt[{\mathrm{3}\:\:}]{\frac{\mathrm{4}}{\mathrm{x}^{\mathrm{3}} }−\mathrm{1}}}\:=\:…

sin-50x-sin-49-x-dx-

Question Number 84163 by john santu last updated on 10/Mar/20 $$\int\:\mathrm{sin}\:\left(\mathrm{50}{x}\right)\:\mathrm{sin}\:^{\mathrm{49}} \left({x}\right)\:{dx}\:? \\ $$ Answered by jagoll last updated on 10/Mar/20 $$\mathrm{sin}\:\mathrm{50x}\:=\:\mathrm{sin}\:\mathrm{49x}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{49x}\:\mathrm{sin}\:\mathrm{x} \\ $$$$\int\:\mathrm{sin}\:^{\mathrm{49}} \mathrm{x}\:\mathrm{sin}\:\mathrm{49x}\:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:+…

solve-1-0-ln-2-e-x-e-4-x-2-dx-pi-k-e-2-k-2-0-ln-3-x-e-2

Question Number 149673 by mnjuly1970 last updated on 06/Aug/21 $$\:\:\:\mathrm{solve}\::: \\ $$$$\left[\:\mathrm{1}\right]\:\:\:\:\boldsymbol{\phi}\::=\:\int_{\mathrm{0}} ^{\:\:\infty\:} \frac{{ln}^{\:\mathrm{2}} \:\left({e}\:{x}\:\right)}{{e}^{\:\mathrm{4}} \:+{x}^{\:\mathrm{2}} }\:{dx}\:=\frac{\pi\:{k}}{{e}^{\:\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{k}:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\left[\:\mathrm{2}\:\right]\:\:\:\Omega\::=\:\int_{\mathrm{0}\:} ^{\:\infty}…

find-the-area-between-the-function-y-2sin2x-1-and-the-x-axis-on-pi-pi-2-

Question Number 84135 by M±th+et£s last updated on 09/Mar/20 $${find}\:{the}\:{area}\:{between}\:{the}\:{function}\: \\ $$$${y}=\mathrm{2}{sin}\mathrm{2}{x}\:−\mathrm{1}\:{and}\:\:{the}\:{x}−{axis}\:\:{on}\:\left[−\pi,\frac{\pi}{\mathrm{2}}\right] \\ $$ Answered by Rio Michael last updated on 09/Mar/20 $$\int_{−\pi} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{2sin}\:\mathrm{2}{x}−\mathrm{1}\right){dx}…