Question Number 217219 by mnjuly1970 last updated on 06/Mar/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{calculate} \\ $$$$\begin{array}{|c|}{\:\:\mathscr{L}\:\:\left(\:\int_{\mathrm{1}} ^{\:\infty} \frac{\:\mathrm{e}^{\:−{tx}} }{{x}}{dx}\:\right)\:\underset{\mathrm{transfom}} {\overset{\mathrm{laplace}} {=}}?\:\:;\:\:{t}>\mathrm{0}\:}\\\hline\end{array} \\ $$$$ \\ $$$$\:\:\: \\ $$…
Question Number 217122 by efronzo1 last updated on 01/Mar/25 $$\:\:\:\:\:\int\:\frac{\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by Frix last updated on 01/Mar/25 $$\int\frac{\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}{\mathrm{cos}\:{x}}{dx}=\int\frac{\sqrt{−\mathrm{1}+\mathrm{2cos}^{\mathrm{2}} \:{x}}}{\mathrm{cos}\:{x}}{dx}\:\overset{\left[{t}=\sqrt{\mathrm{2}}\mathrm{sin}\:{x}\right]} {=} \\ $$$$=\sqrt{\mathrm{2}}\int\frac{\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{\mathrm{2}−{t}^{\mathrm{2}}…
Question Number 216990 by MathematicalUser2357 last updated on 26/Feb/25 $$\left(\mathrm{1}\right)\:\int\left(\mathrm{sec}^{\mathrm{2}} {x}\centerdot\sqrt{\mathrm{tan}\:{x}}\right){dx}=? \\ $$ Commented by MathematicalUser2357 last updated on 26/Feb/25 $$\left(\mathrm{2}\right)\:\mathrm{Go}\:\mathrm{to}\:\underline{\mathrm{https}://\mathrm{playentry}.\mathrm{org}/\mathrm{project}/\mathrm{67a8a3c0d78abe99420525f0}} \\ $$$$\mathrm{and}\:\mathrm{press}\:\mathrm{the}\:\mathrm{play}\:\mathrm{button}\:\mathrm{and}\:\mathrm{screenshot}\:\mathrm{and}\:\mathrm{give}\:\mathrm{the}\:\mathrm{screenshot}\:\mathrm{to}\:\mathrm{me} \\ $$…
Question Number 216886 by Engr_Jidda last updated on 23/Feb/25 $${Evaluate}\:\frac{\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\int_{\mathrm{0}} ^{{k}} \left(\mathrm{4}{u}+\mathrm{1}\right){du}\right)}{\mathrm{5}^{\mathrm{2}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{2}}{{m}^{\mathrm{2}} +\mathrm{2}{m}}\right)^{{n}−\mathrm{1}} }\int_{{sin}^{−\mathrm{1}} \left(\frac{−\sqrt{\mathrm{2}}}{\mathrm{2}}\right)} ^{\frac{\pi}{\mathrm{2}}{cos}\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}−{sec}\theta{sin}\theta}{\frac{{tan}\theta+{cot}\theta}{\varrho^{\theta} −\varrho^{\pi{i}}…
Question Number 216819 by MrGaster last updated on 22/Feb/25 $$\mathrm{Prove}:\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{K}}\left({x}\right)}{\:\sqrt{\mathrm{3}−{x}}}{dx}=\frac{\mathrm{1}}{\mathrm{96}\pi\sqrt{\mathrm{3}}}×\Gamma\left(\frac{\mathrm{1}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{3}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{7}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{11}}{\mathrm{24}}\right) \\ $$ Answered by MrGaster last updated on 24/May/25 $$\boldsymbol{\mathrm{K}}\left({x}\right)=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{d}\theta}{\:\sqrt{\mathrm{1}−{x}\:\mathrm{sin}^{\mathrm{2}} \theta}}…
Question Number 216799 by OPAVdx last updated on 20/Feb/25 Commented by MathematicalUser2357 last updated on 22/Feb/25 $${sen}? \\ $$ Answered by MATHEMATICSAM last updated on…
Question Number 216776 by MrGaster last updated on 19/Feb/25 Answered by MathematicalUser2357 last updated on 22/Feb/25 $$\mathrm{0}.\mathrm{308425}\:\mathrm{is}\:\mathrm{what}\:\mathrm{I}\:\mathrm{get}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 216774 by Nadirhashim last updated on 19/Feb/25 $$\:\:\boldsymbol{{find}}\:\int\:\frac{\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)\:}{\mathrm{1}+\boldsymbol{{sec}}^{\mathrm{4}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\: \\ $$ Answered by MathematicalUser2357 last updated on 25/Feb/25 $$\frac{\mathrm{1}}{\mathrm{2}}\left\{−\mathrm{2}{x}+\sqrt{\mathrm{1}−{i}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{tan}\left({x}\right)}{\:\sqrt{\mathrm{1}−{i}}}\right)+\sqrt{\mathrm{1}+{i}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{tan}\left({x}\right)}{\:\sqrt{\mathrm{1}+{i}}}\right)\right\}+{C} \\…
Question Number 216772 by Nadirhashim last updated on 19/Feb/25 $$\:\:\boldsymbol{{find}}\:\int\frac{\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)\:}{\mathrm{1}−\boldsymbol{{sec}}^{\mathrm{4}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\:\: \\ $$ Answered by MrGaster last updated on 19/Feb/25 $$\:\int\frac{\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)\:}{\mathrm{1}−\boldsymbol{{sec}}^{\mathrm{4}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\:=\int\frac{\mathrm{tan}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−\left(\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}}…
Question Number 216754 by Tawa11 last updated on 17/Feb/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{x}\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by issac last updated on 18/Feb/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}}…