Question Number 197436 by horsebrand11 last updated on 17/Sep/23 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{dx}}{\mathrm{3}+\mathrm{tan}\:\mathrm{x}}\:=? \\ $$ Answered by Frix last updated on 17/Sep/23 $$\int\frac{{dx}}{\mathrm{3}+\mathrm{tan}\:{x}}\:\overset{{t}=\mathrm{tan}\:{x}} {=}\:\int\frac{{dt}}{\left({t}+\mathrm{3}\right)\left({t}^{\mathrm{2}} +\mathrm{1}\right)}= \\…
Question Number 197431 by mnjuly1970 last updated on 17/Sep/23 $$ \\ $$$$ \\ $$$$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \left(\:\mathrm{1}+\:{x}^{\mathrm{2}} \:+\:{y}^{\:\mathrm{2}} +{z}^{\:\mathrm{2}} \right)^{\:−\frac{\mathrm{5}}{\mathrm{2}}} {dxdydz}=? \\…
Question Number 197383 by universe last updated on 15/Sep/23 $$\:{evaluate}\:\:\int_{\mathrm{1}/\mathrm{4}} ^{\mathrm{1}} \int_{\sqrt{{x}−{x}^{\mathrm{2}} }} ^{\sqrt{{x}}} \frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }{dydx}\:=\:?? \\ $$ Commented by Frix last updated…
Question Number 197376 by megrex last updated on 15/Sep/23 $${Does}\:{anyone}\:{know}\:{how}\:{to}\:{prove}\:{this}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\int\int_{{V}} \:\frac{{dxdydz}}{\mathrm{1}+{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} }\:=\frac{\Gamma^{\mathrm{4}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}^{\mathrm{4}} } \\ $$$${where}\:{V}\:{is}\:{the}\:{unit}\:{cube}\:\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} \\ $$$${Thankyou}. \\ $$$$ \\…
Question Number 197343 by Mathspace last updated on 14/Sep/23 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}\right).{ln}\left({sinx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197292 by universe last updated on 12/Sep/23 $$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{{nx}^{{n}−\mathrm{1}} }{\mathrm{1}+{x}}{dx}\:\:=\:\:\:? \\ $$ Answered by witcher3 last updated on 12/Sep/23 $$\mathrm{2x}\leqslant\mathrm{1}+\mathrm{x}\leqslant\mathrm{2},\forall\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right] \\…
Question Number 197239 by universe last updated on 10/Sep/23 Answered by mahdipoor last updated on 11/Sep/23 $$\overset{\frac{{d}}{{dx}}} {\Rightarrow}{xsin}^{{n}} {x}=\left(\frac{{xsin}^{{n}} {x}}{{n}}−\frac{\left({n}−\mathrm{1}\right){xsin}^{{n}−\mathrm{2}} {cos}^{\mathrm{2}} {x}}{{n}}−\frac{{sin}^{{n}−\mathrm{1}} {xcosx}}{{n}}\right) \\ $$$$+\left(\frac{{sin}^{{n}−\mathrm{1}}…
Question Number 197212 by MathematicalUser2357 last updated on 10/Sep/23 $$\mathrm{Is}\:\int{f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{{x}} \underset{{x}\rightarrow{t}} {\mathrm{lim}}{f}\left({x}\right){dt}? \\ $$ Commented by mahdipoor last updated on 10/Sep/23 $${if}\:\:\:\:\:{limf}\left({x}\right),{x}\rightarrow{t}={f}\left({t}\right) \\ $$$$\int{f}\left({x}\right){dx}=\int_{\mathrm{0}}…
Question Number 197190 by universe last updated on 10/Sep/23 $$\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{3}} \sqrt{\mathrm{1}−{x}^{\mathrm{7}} }\:{dx}\:−\:\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:^{\mathrm{7}} \sqrt{\mathrm{1}−{x}^{\mathrm{3}} }\:{dx}\:\:=\:\:? \\ $$ Commented by Frix last updated…
Question Number 197191 by tri26112004 last updated on 10/Sep/23 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{7}}{dx} \\ $$ Answered by Frix last updated on 10/Sep/23 $${x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{7}=\left({x}−{a}\right)\left({x}^{\mathrm{2}} +{ax}+{b}\right) \\ $$$${a}=−\frac{\sqrt[{\mathrm{3}}]{\mathrm{7}+\mathrm{3}\sqrt{\mathrm{5}}}+\sqrt[{\mathrm{3}}]{\mathrm{7}−\mathrm{3}\sqrt{\mathrm{5}}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}};\:{b}=−\frac{\mathrm{7}}{{a}}…