Question Number 69044 by mathmax by abdo last updated on 18/Sep/19 $$\left.\mathrm{1}\right)\:{let}\:{f}\left({a}\right)\:=\int\sqrt{{a}+{tanx}}{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({a}\right)\:=\int\:\:\frac{{dx}}{\:\sqrt{{a}+{tanx}}} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int\sqrt{\mathrm{2}+{tanx}}{dx}\:{and}\:\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{2}+{tanx}}} \\ $$ Answered by mind is power…
Question Number 134570 by liberty last updated on 05/Mar/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{y}} ^{\:\mathrm{y}^{\mathrm{1}/\mathrm{3}} } \sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}\:\mathrm{dx}\:\mathrm{dy}\:=?\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69027 by rajesh4661kumar@gmail.com last updated on 18/Sep/19 Commented by mathmax by abdo last updated on 18/Sep/19 $${I}\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} {sinxdx}\:−\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mid{sinx}\mid{dx}\:\:{but} \\ $$$$\int_{\mathrm{0}}…
Question Number 134544 by nabeelabashir last updated on 05/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134547 by EDWIN88 last updated on 05/Mar/21 $$\mathscr{R}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{3}{a}} {x}\:\sqrt{\frac{\mathrm{3}{a}−{x}}{{x}+{a}}}\:{dx}\: \\ $$ Answered by liberty last updated on 05/Mar/21 $$\mathrm{by}\:\mathrm{change}\:\mathrm{of}\:\mathrm{variable}\: \\ $$$$\:\mathrm{let}\:\sqrt{\frac{\mathrm{3}{a}−{x}}{{x}+{a}}}\:={h}\:\Rightarrow\:{x}=\frac{−{ah}^{\mathrm{2}} +\mathrm{3}{a}}{{h}^{\mathrm{2}}…
Question Number 68970 by Peculiar last updated on 17/Sep/19 $$\int\frac{\mathrm{3}{t}^{\mathrm{2}} }{\left(\mathrm{1}+{t}\right)^{\mathrm{15}} }\:{dt} \\ $$ Answered by Kunal12588 last updated on 17/Sep/19 $$\mathrm{1}+{t}={u} \\ $$$$\Rightarrow{t}={u}−\mathrm{1} \\…
Question Number 68967 by aliesam last updated on 17/Sep/19 Answered by mind is power last updated on 17/Sep/19 $${tg}\left(\frac{{x}}{\mathrm{2}}\right)={t} \\ $$$${dx}=\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}} } \\ $$$$\Rightarrow{sin}\left({x}\right)=\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:{cos}\left({x}\right)=\frac{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 68956 by A8;15: last updated on 17/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134474 by rs4089 last updated on 04/Mar/21 $${Evaluate}\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}^{{a}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 04/Mar/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 134456 by bramlexs22 last updated on 03/Mar/21 $$\underset{−\infty} {\int}^{\:\:\:\:\infty} \frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:\mathrm{dx}\:? \\ $$ Commented by EDWIN88 last updated on 04/Mar/21 $$=\:\frac{\mathrm{3}\pi}{\mathrm{4}} \\…