Question Number 221 by 123456 last updated on 25/Jan/15 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\ $$ Answered by mreddy last updated on 16/Dec/14 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\…
Question Number 216 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate} \\ $$$$\underset{−\infty} {\overset{+\infty} {\int}}{f}\left({x}\right){dx} \\ $$$$\mathrm{where} \\ $$$${f}\left({x}\right)=\begin{cases}{{e}^{{x}} }&{{x}\leqslant\mathrm{0}}\\{\mathrm{1}+{x}}&{\mathrm{0}<{x}\leqslant\mathrm{1}}\\{\mathrm{1}+{x}^{\mathrm{2}} }&{\mathrm{1}<{x}\leqslant\mathrm{2}}\\{\mathrm{5}}&{\mathrm{2}<{x}\leqslant\mathrm{5}}\\{\frac{\mathrm{5}}{\mathrm{1}+\left({x}−\mathrm{5}\right)^{\mathrm{2}} }}&{{x}>\mathrm{5}}\end{cases} \\ $$ Answered by…
Question Number 131286 by mnjuly1970 last updated on 03/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:{calculus}\:…. \\ $$$$\:\:\:\:\:{find}\:::\:\:{i}::\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −\mathrm{1}}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ii}::\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{4}} −\mathrm{1}}\right)=? \\ $$$$\:\:\:\: \\…
Question Number 65740 by rajesh4661kumar@gmail.com last updated on 03/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $${let}\:{A}\:=\:\int\:\:\:\frac{{dx}}{\frac{\mathrm{1}}{{cosx}}\:+{sinx}}\:\Rightarrow\:{A}\:=\int\:\frac{{cosx}}{\mathrm{1}+{cosx}\:{sinx}}{dx}\:{changement} \\ $$$${tan}\left(\frac{{x}}{\mathrm{2}\:}\right)\:={t}\:{give}\:{A}\:=\int\:\:\:\frac{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{1}+\frac{\mathrm{2}{t}\left(\mathrm{1}−{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 65736 by malwaan last updated on 03/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}\:+\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} }\:\boldsymbol{{dx}}\:=\:? \\ $$ Commented by Souvik Ghosh last updated on 03/Aug/19 $${let}\:\:\:{u}=\mathrm{2}{x}\Leftrightarrow{du}=\mathrm{2}{dx} \\…
Question Number 191 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:\underset{\mathrm{C}} {\int}\frac{{z}^{\mathrm{2}} \mathrm{sin}\:{z}\:\mathrm{cos}\:{z}}{\left({z}^{\mathrm{2}} +\mathrm{1}\right)\left({z}^{\mathrm{2}} −\mathrm{1}\right)}{dz}\: \\ $$$$\mathrm{where}\:\mathrm{C}=\left\{{z}\in\mathbb{C}\mid\mid{z}\mid=\mathrm{2}\right\} \\ $$ Answered by nileshkulkarni last updated on 15/Dec/14…
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Question Number 65729 by aliesam last updated on 02/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $$\left.{a}\right)\:\:{let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:{e}^{{ix}} \:{x}^{−\alpha} \:{dx}\:\:\Rightarrow{f}\left(\alpha\right)\:=_{{ix}\:={t}} \:\:\:\int_{\mathrm{0}} ^{\infty}…
Question Number 131245 by Ahmed1hamouda last updated on 02/Feb/21 $$\:\mathrm{Find}\: \\ $$$$\:\:\:\:\int_{−\mathrm{b}} ^{\mathrm{b}} \int_{−\mathrm{a}} ^{\mathrm{a}} \frac{\mathrm{d}{xdy}}{\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{h}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} } \\ $$ Answered by Ar…
Question Number 131247 by bramlexs22 last updated on 03/Feb/21 $$\left(\mathrm{1}\right)\:\psi\:=\:\int\:\frac{{dx}}{\mathrm{1}−\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}=? \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}}{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}\:=? \\ $$$$\left(\mathrm{3}\right)\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{3}/\mathrm{2}} +\mathrm{1}}\:{dx}\:=?\: \\ $$ Answered by liberty…