Question Number 54374 by maxmathsup by imad last updated on 02/Feb/19 $${calculate}\:{h}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left({at}\right)}{{ch}\left(\frac{{t}}{\mathrm{2}}\right)}{dt}\:. \\ $$ Commented by Abdo msup. last updated on 08/Feb/19 $${h}\left({a}\right)=_{\frac{{t}}{\mathrm{2}}={x}}…
Question Number 54372 by maxmathsup by imad last updated on 02/Feb/19 $${let}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{{x}+{sint}}{dt}\:\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\left({x}+{sint}\right)^{\mathrm{2}} }\:{dt}\: \\ $$$$\left.\mathrm{3}\right)\:{calculste}\:{for}\:{n}\in{N}\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sint}}{\left({x}+{sint}\right)^{{n}}…
Question Number 54371 by maxmathsup by imad last updated on 02/Feb/19 $${prove}\:{that}\:{ln}\left({z}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{z}−\mathrm{1}}{\mathrm{1}+{t}\left({z}−\mathrm{1}\right)}{dt}\:. \\ $$ Commented by maxmathsup by imad last updated on 02/Feb/19…
Question Number 54367 by maxmathsup by imad last updated on 02/Feb/19 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\left[{t}\right]}{{t}}\:{t}^{−{p}} {dt}\:{interms}\:{of}\:\xi\left({p}\right)\:{with}\:{p}>\mathrm{0}\:. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 119852 by benjo_mathlover last updated on 27/Oct/20 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{{n}}} {\:}}{x}^{{x}+\mathrm{1}} \:{dx}\:=? \\ $$ Answered by Olaf last updated on 27/Oct/20 $$\int_{\mathrm{0}}…
Question Number 119821 by bemath last updated on 27/Oct/20 $$\:\underset{−\mathrm{3}} {\overset{\mathrm{0}} {\int}}\:\frac{\mathrm{6}{x}−\mathrm{6}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}}\:{dx}\:=? \\ $$ Answered by bobhans last updated on 27/Oct/20 $$\:\underset{−\mathrm{3}} {\overset{\mathrm{0}} {\int}}\:\frac{\mathrm{6}\left({x}−\mathrm{1}\right)}{\:\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 54273 by rahul 19 last updated on 01/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Feb/19 $$\frac{{df}}{{dx}}={f}\left({x}\right)+\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$$$\frac{{df}}{{dx}}={f}\left({x}\right)+{a} \\ $$$$\frac{{df}}{{f}\left({x}\right)+{a}}={dx} \\…
Question Number 54259 by 951172235v last updated on 01/Feb/19 Commented by Meritguide1234 last updated on 01/Feb/19 Answered by rahul 19 last updated on 01/Feb/19 $$\mathrm{1}.…
Question Number 119784 by bemath last updated on 27/Oct/20 $$\:\:\int\:\frac{{dx}}{\:\sqrt{\left(\mathrm{4}{x}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$$$ \\ $$ Answered by bobhans last updated on 27/Oct/20 $$\int\:\frac{{dx}}{\:\left(\mathrm{4}−\left(\mathrm{2}−{x}\right)^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 54248 by rahul 19 last updated on 01/Feb/19 Commented by rahul 19 last updated on 01/Feb/19 $$\left.{Ans}.\:{for}\:\mathrm{3}\right)\rightarrow\:\mathrm{2}\pi^{\mathrm{2}} . \\ $$$$\left.{for}\:\mathrm{2}\right)\rightarrow\:{put}\:{x}=\mathrm{tan}\theta\:{and}\:{then}\:{use} \\ $$$${the}\:{property}\:{of}\:{replacing}\:{x}\:{by}\:{a}+{b}−{x}. \\…