Question Number 13977 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 25/May/17 Commented by prakash jain last updated on 26/May/17 $$\int\frac{\mathrm{3}+{x}^{\mathrm{2}} }{\mathrm{2}+{x}^{\mathrm{3}} }{dx} \\ $$$$\int\frac{\mathrm{3}}{\left(\mathrm{2}^{\mathrm{1}/\mathrm{3}} \right)^{\mathrm{3}} +{x}^{\mathrm{3}} }{dx}+\int\frac{{x}^{\mathrm{2}}…
Question Number 145044 by mathmax by abdo last updated on 01/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\mathrm{2x}} \sqrt{\mathrm{1}+\mathrm{sinx}}\mathrm{dx} \\ $$ Answered by qaz last updated on 02/Jul/21 $$\int_{\mathrm{0}}…
Question Number 145046 by mathmax by abdo last updated on 01/Jul/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\mid\mathrm{cosx}\:+\mathrm{sinx}\mid\mathrm{e}^{−\mathrm{x}} \:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 79500 by ubaydulla last updated on 25/Jan/20 $$\int\left(\mathrm{cot}\:^{\mathrm{2}} {x}+\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$ Answered by john santu last updated on 25/Jan/20 $$\int\mathrm{cot}\:^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right){dx}\:=…
Question Number 13960 by tawa tawa last updated on 25/May/17 $$\int_{\:\:\:\mathrm{0}} ^{\:\frac{\mathrm{a}}{\mathrm{2}}} \:\:\:\mathrm{x}^{\mathrm{2}} \left(\mathrm{a}^{\mathrm{2}} \:−\:\mathrm{x}^{\mathrm{2}} \right)^{−\mathrm{3}/\mathrm{2}} \:\:\mathrm{dx} \\ $$ Answered by ajfour last updated on…
Question Number 79485 by ubaydulla last updated on 25/Jan/20 $$\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx} \\ $$ Answered by jagoll last updated on 25/Jan/20 $$\int\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\right)\mathrm{dx}= \\…
Question Number 144997 by qaz last updated on 01/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}}\mathrm{dx}=\frac{\pi}{\mathrm{2}}\mathrm{G}−\frac{\mathrm{33}}{\mathrm{32}}\zeta\left(\mathrm{3}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144985 by imjagoll last updated on 01/Jul/21 $$\:\int\:\frac{\left(\mathrm{2}+\sqrt{\mathrm{x}}\right)}{\left(\mathrm{x}+\mathrm{1}+\sqrt{\mathrm{x}}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by mathmax by abdo last updated on 01/Jul/21 $$\mathrm{f}\left(\mathrm{a}\right)=\int\:\:\:\frac{\mathrm{2}+\sqrt{\mathrm{x}}}{\mathrm{x}+\mathrm{a}+\sqrt{\mathrm{x}}}\:\:\:\mathrm{with}\:\mathrm{a}>\frac{\mathrm{1}}{\mathrm{4}}\:\Rightarrow\mathrm{f}^{'} \left(\mathrm{a}\right)=−\int\:\:\frac{\mathrm{2}+\sqrt{\mathrm{x}}}{\left(\mathrm{x}+\mathrm{a}+\sqrt{\mathrm{x}}\right)^{\mathrm{2}} }\mathrm{dx}\:\Rightarrow…
Question Number 144975 by mim24 last updated on 01/Jul/21 Answered by ArielVyny last updated on 01/Jul/21 $$\int{u}'×{u}^{{n}} {du}=\frac{\mathrm{1}}{{n}+\mathrm{1}}{u}^{{n}+\mathrm{1}} +{cte} \\ $$$$\int\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\left({x}+{ln}\left({x}\right)\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{lnx}\right)^{\mathrm{2}} \\ $$ Answered by…
Question Number 79413 by rajesh4661kumar@gmail.com last updated on 25/Jan/20 Commented by john santu last updated on 25/Jan/20 $$\left(\frac{\mathrm{cos}\:{x}\mathrm{sin}\:{x}}{\mathrm{cos}\:\mathrm{2}{x}\left(\mathrm{cos}^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{2}} {x}\right)\:}\right)^{\mathrm{2}} = \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}.\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}{\mathrm{cos}\:^{\mathrm{4}} \mathrm{2}{x}}\:=\frac{\mathrm{1}}{\mathrm{4}}\mathrm{tan}\:^{\mathrm{2}}…