Question Number 139283 by qaz last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{ln}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{8}{a}}\left(\pi^{\mathrm{2}} +\mathrm{4}{ln}^{\mathrm{2}} {a}\right)\:\:\:\:\:\:\:\:\:,{a}>\mathrm{0} \\ $$ Answered by Ar Brandon last updated…
Question Number 139282 by qaz last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{ln}\:{x}}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{2}{a}}\centerdot{ln}\:{a}\:\:\:\:\:\:\:\:\:\:,{a}>\mathrm{0}\: \\ $$ Answered by Ar Brandon last updated on 25/Apr/21 $$\Omega=\int_{\mathrm{0}}…
Question Number 139272 by bobhans last updated on 25/Apr/21 $$ \\ $$What is the area bounded by the parabola y^2=4ax and x^2 = 4ay? Answered…
Question Number 139259 by bobhans last updated on 25/Apr/21 $$\:\int\:\frac{\mathrm{cos}\:\mathrm{x}+\sqrt[{\mathrm{3}}]{\mathrm{7}}}{\mathrm{sin}\:\mathrm{x}+\sqrt{\mathrm{6}}}\:\mathrm{dx}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 25/Apr/21 $$\int\frac{{cosx}+\sqrt[{\mathrm{3}}]{\mathrm{7}}}{{sinx}+\sqrt{\mathrm{6}}}{dx}={log}\left({sinx}+\sqrt{\mathrm{6}}\right)+\sqrt[{\mathrm{3}}]{\mathrm{7}}\:\int\frac{\mathrm{1}}{{sinx}+\sqrt{\mathrm{6}}}{dx} \\ $$$$={log}\left({sinx}+\sqrt{\mathrm{6}}\right)+\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{7}}\:\int\frac{\mathrm{1}}{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\sqrt{\mathrm{6}}}.\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:{tan}\frac{{x}}{\mathrm{2}}={t}…
Question Number 73715 by Learner-123 last updated on 15/Nov/19 $${Evaluate}\:{the}\:{integral}\:: \\ $$$$\underset{\:\mathbb{R}} {\int}\int\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{14}{xy}+\mathrm{8}{y}^{\mathrm{2}} \right){dxdy}\:{for}\:{the}\:{region} \\ $$$$\mathbb{R}\:\mathrm{in}\:{the}\:\mathrm{1}{st}\:{quadrant}\:{bounded}\:{by}\:{the} \\ $$$${lines}\:{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{1},{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{3},{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x} \\ $$$${and}\:{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x}+\mathrm{1}\:. \\ $$ Commented by…
Question Number 139248 by ajfour last updated on 24/Apr/21 $$\int_{{a}} ^{\:{b}} {f}\left({t}\right){g}'\left({t}\right){dt}=\:? \\ $$ Answered by mathmax by abdo last updated on 25/Apr/21 $$\int_{\mathrm{a}} ^{\mathrm{b}}…
Question Number 139224 by mnjuly1970 last updated on 24/Apr/21 $$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)}{{x}}{dx} \\ $$$$\:\:\:\phi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{3}} \right)−{ln}\left(\mathrm{1}−{x}\right)}{{x}}{dx} \\ $$$$\:\:\:\:=\Omega+\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\:\:\:\:\Omega=−\Sigma\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{\mathrm{3}{n}−\mathrm{1}}…
Question Number 73689 by ajfour last updated on 14/Nov/19 $$\int_{−\mathrm{1}} ^{\:\:\mathrm{1}} \left(\mathrm{2}+{x}\right)\mathrm{sin}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{3}−\mathrm{3}{x}^{\mathrm{2}} }}{\mathrm{2}+{x}}\right){dx}\:=\:? \\ $$ Answered by mind is power last updated on 15/Nov/19…
Question Number 139217 by mnjuly1970 last updated on 24/Apr/21 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:…..\:{nice}\:….\:….\:{math}…. \\ $$$$\:\:\:{prove}\:{that}: \\ $$$$\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{ln}\left(\mathrm{1}+{sin}\left({x}\right).{cos}\left({x}\right)\right)}{{tan}\left({x}\right)}{dx}=\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{72}} \\ $$ Commented by liki last…
Question Number 8114 by uchechukwu okorie favour last updated on 30/Sep/16 $${Evaluate}\:\int\mathrm{cos}\:^{\mathrm{6}} {x} \\ $$ Answered by sandy_suhendra last updated on 30/Sep/16 Answered by prakash…