Question Number 203714 by K1000 last updated on 26/Jan/24 $$\int\mathrm{2}{x}^{\mathrm{2}} \\ $$ Answered by Frix last updated on 26/Jan/24 $$\int{ax}^{{n}} {dx}={a}\int{x}^{{n}} {dx}=\frac{{ax}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}+{C} \\ $$…
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Question Number 203564 by mnjuly1970 last updated on 22/Jan/24 $$ \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\:\mathrm{3}} \left({x}\right)}{{x}^{\:\mathrm{2}} }\:{dx}=\:?\:\:\:\:\: \\ $$ Answered by Mathspace last updated on 23/Jan/24…
Question Number 203385 by patrice last updated on 18/Jan/24 Answered by Mathspace last updated on 18/Jan/24 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:\Rightarrow{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{3}{n}}…
Question Number 203349 by Mathspace last updated on 17/Jan/24 $${calculate}\:\int\int_{\left[\mathrm{0},{a}\right]^{\mathrm{2}} } \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy} \\ $$$${can}\:{you}\:{find}\:\int_{\mathrm{0}} ^{{a}} {e}^{−{x}^{\mathrm{2}} } {dx}\:\:\:\:? \\ $$$${a}>\mathrm{0} \\ $$…
Question Number 203186 by lorance last updated on 11/Jan/24 $${f}\left({x}\right)=\left\{_{\mathrm{2}\:\:\:\:\:\:\:\:{x}=\mathrm{1}} ^{\mathrm{7}\:\:\:\:\:\:\:\:{x}\neq\mathrm{1}\:\:\:\:\:} \Rightarrow\:\int_{\mathrm{0}} ^{\:\mathrm{4}} {f}\left({x}\right){dx}=?\right. \\ $$ Answered by mr W last updated on 12/Jan/24 $$\int_{\mathrm{0}}…
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Question Number 202930 by Calculusboy last updated on 06/Jan/24 Answered by MathematicalUser2357 last updated on 06/Jan/24 $$\mathrm{No}\:\mathrm{antiderivative}\:\mathrm{could}\:\mathrm{be}\:\mathrm{found}\:\mathrm{within}\:\mathrm{the}\:\mathrm{given} \\ $$$$\mathrm{time}\:\mathrm{limit},\:\mathrm{or}\:\mathrm{all}\:\mathrm{supported}\:\mathrm{integration}\:\mathrm{methods} \\ $$$$\mathrm{were}\:\mathrm{tried}\:\mathrm{unsuccessfully}.\:\mathrm{Note}\:\mathrm{that}\:\mathrm{many}\:\mathrm{functions} \\ $$$$\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{an}\:\mathrm{elementary}\:\mathrm{antiderivative}. \\ $$…
Question Number 202882 by dimentri last updated on 05/Jan/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by cortano12 last updated on 05/Jan/24 $$\:\:\begin{cases}{\mathrm{5}\underset{\mathrm{3}} {\overset{\mathrm{6}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{10}}\\{\mathrm{5}\underset{\mathrm{1}} {\overset{\mathrm{6}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{2}}\end{cases} \\…
Question Number 202591 by Calculusboy last updated on 30/Dec/23 Answered by mr W last updated on 30/Dec/23 $$\frac{{dy}}{{dx}}+\mathrm{1}+\frac{{y}}{{x}}=\mathrm{0} \\ $$$${let}\:{y}={xt} \\ $$$$\frac{{dy}}{{dx}}={t}+{x}\frac{{dt}}{{dx}} \\ $$$${t}+{x}\frac{{dt}}{{dx}}+\mathrm{1}+{t}=\mathrm{0} \\…