Menu Close

Category: Integration

nice-calculus-calculation-of-2-6-1-x-2-x-4-x-6-1-3-cos-2021-pix-x-2-8x-20-dx-solution-x-4-t-x-6-t-2

Question Number 137930 by mnjuly1970 last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:…\:…\:{calculus}….. \\ $$$$\:\:\:\:\:{calculation}\:{of}::: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{2}} ^{\:\mathrm{6}} \:\frac{\mathrm{1}+\left(\sqrt[{\mathrm{3}}]{\left({x}−\mathrm{2}\right)\left({x}−\mathrm{4}\right)\left({x}−\mathrm{6}\right)}\:\right){cos}^{\mathrm{2021}} \left(\pi{x}\right)}{{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{20}}{dx}=? \\ $$$$\:\:\:\:\:{solution}:: \\ $$$$\:\:\:\:\:{x}−\mathrm{4}={t}\:\Rightarrow\left\{_{\:{x}=\mathrm{6}\:\Rightarrow\:{t}=\mathrm{2}} ^{{x}=\mathrm{2}\:\Rightarrow{t}=−\mathrm{2}} \right. \\…

0-2-x-2-cos-xdx-

Question Number 137926 by brayan last updated on 08/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} {x}^{\mathrm{2}} \mathrm{cos}\:{xdx}= \\ $$ Answered by Ñï= last updated on 08/Apr/21 $$\frac{\mathrm{1}}{{D}}{x}^{\mathrm{2}} \mathrm{cos}\:{x}={Re}\left({e}^{{ix}} \frac{\mathrm{1}}{{D}+{i}}{x}^{\mathrm{2}}…

Integrate-x-sec-2-x-2-

Question Number 6841 by Tawakalitu. last updated on 30/Jul/16 $${Integrate}:\:\:{x}\:{sec}^{\mathrm{2}} \left({x}^{\mathrm{2}} \right) \\ $$$$ \\ $$ Commented by Tawakalitu. last updated on 30/Jul/16 $${I}\:{have}\:{solve}\:{this}\:{one}.\:{i}\:{got}\:…\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:{tan}\left({x}^{\mathrm{2}} \right)\:+\:{C}…