Category: Integration

Question Number 172088 by Mikenice last updated on 23/Jun/22 Answered by Joepkollie last updated on 23/Jun/22 $$\:\:\:\boldsymbol{{solution}}.. \\ $$$$\:\:\:\boldsymbol{{y}}=\boldsymbol{\mathrm{e}}^{\boldsymbol{{u}}\:} \Rightarrow\Rightarrow\boldsymbol{{y}}'=\boldsymbol{\mathrm{e}}^{\boldsymbol{{u}}} \bullet\boldsymbol{{u}}' \\ $$$$\:\:\:\:\boldsymbol{{y}}'=\mathrm{cos}\boldsymbol{{x}\mathrm{e}}^{\mathrm{sin}\boldsymbol{{x}}} .. \\…

Question Number 40952 by Raj Singh last updated on 30/Jul/18 Commented by abdo mathsup 649 cc last updated on 30/Jul/18 $${let}\:{I}\:=\:\int\:\:\:\:\frac{{dx}}{\left(\mathrm{9}−{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$$${I}\:=_{{x}=\mathrm{3}{sin}\theta}…

Question Number 172012 by Mikenice last updated on 23/Jun/22 $${find} \\ $$$$\int{e}^{{x}} {sinxdx} \\ $$ Answered by puissant last updated on 23/Jun/22 $${J}=\int{e}^{{x}} {sinxdx} \\…

Question Number 172011 by Mikenice last updated on 23/Jun/22 $${find}\:{integrate}: \\ $$$$\int{x}^{\mathrm{2}} {e}^{{x}} {dx} \\ $$ Answered by puissant last updated on 23/Jun/22 $${P}\:=\:\int{x}^{\mathrm{2}} {e}^{{x}}…

Question Number 171971 by ilhamQ last updated on 22/Jun/22 $$\int\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}}\:{dx}=… \\ $$ Answered by cortano1 last updated on 22/Jun/22 $$\:\:\frac{{x}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right)}\:=\:\frac{{a}}{{x}+\mathrm{1}}\:+\:\frac{{b}}{{x}+\mathrm{3}} \\ $$$$\:{a}\:=\:\frac{−\mathrm{1}}{−\mathrm{1}+\mathrm{3}}\:=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:{b}=\frac{−\mathrm{3}}{−\mathrm{3}+\mathrm{1}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}…