Question Number 53112 by maxmathsup by imad last updated on 21/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{1}+\mathrm{2}{sinx}}{\mathrm{3}\:+\mathrm{2}{cosx}}{dx} \\ $$$${let}\:{A}\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{1}+\mathrm{2}{sinx}}{\mathrm{3}\:+\mathrm{2}{cosx}}{dx}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}+\frac{\mathrm{4}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{3}+\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 53089 by Tawa1 last updated on 17/Jan/19 $$\int_{\:\frac{\pi}{\mathrm{2}}\:} ^{\:\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{5}\:+\:\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{tanh}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{3}}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53080 by Abdo msup. last updated on 17/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{cos}^{\mathrm{2}} {x}}{\mathrm{2}+\mathrm{3}{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Commented by maxmathsup by imad last updated on 17/Jan/19…
Question Number 53081 by cesar.marval.larez@gmail.com last updated on 17/Jan/19 Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jan/19 $$\left.\mathrm{1}\right)\int{e}^{\mathrm{2}{x}} {sinxdx} \\ $$$${e}^{\mathrm{2}{x}} \int{sinxdx}−\int\left[\frac{{d}\left({e}^{\mathrm{2}{x}} \right)}{{dx}}\int{sinxdx}\right]{dx} \\ $$$$={e}^{\mathrm{2}{x}} ×−{cosx}−\int\mathrm{2}{e}^{\mathrm{2}{x}}…
Question Number 53078 by gunawan last updated on 16/Jan/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\:{dx}=… \\ $$ Commented by MJS last updated on 17/Jan/19 $$\approx.\mathrm{774606} \\…
Question Number 184136 by greougoury555 last updated on 03/Jan/23 $$\:\underset{\mathrm{0}} {\overset{\mathrm{2}{n}\pi} {\int}}\:{max}\left(\mathrm{sin}\:{x},\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:{x}\right)\right)\:{dx}\:=?\: \\ $$$$\:\left[\:{n}\in\:{I}\:\right]\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 184112 by cortano1 last updated on 03/Jan/23 $$\:\:\int\:\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{5}/\mathrm{6}} \left({x}+\mathrm{2}\right)^{\mathrm{7}/\mathrm{6}} }\:=? \\ $$ Commented by sahalu last updated on 03/Jan/23 $$\:\:\int\:\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{5}/\mathrm{6}} \left({x}+\mathrm{2}\right)^{\mathrm{7}/\mathrm{6}} }\:=?\left.\begin{matrix}{\int}\\{}\end{matrix}\right\} \\…
Question Number 118575 by bramlexs22 last updated on 18/Oct/20 $$\:\:\int\:\mathrm{cos}\:\left(\mathrm{2cot}^{−\mathrm{1}} \sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:\right)\:{dx}\:? \\ $$ Answered by benjo_mathlover last updated on 18/Oct/20 $${set}\:\mathrm{cot}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\right)\:=\:\phi\:\Rightarrow\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:=\:\mathrm{cot}\:\phi \\ $$$$\Rightarrow\:\mathrm{cot}\:^{\mathrm{2}} \phi\:=\:\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\:,\:\mathrm{tan}\:^{\mathrm{2}}…
Question Number 118566 by benjo_mathlover last updated on 18/Oct/20 $$\:\:{solve}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}}\:\sqrt{\mathrm{1}−{x}}\:}\:. \\ $$ Commented by benjo_mathlover last updated on 18/Oct/20 $${in}\:{other}\:{way}\:{by}\:{substitute}\:{trigonometri} \\ $$$${letting}\:{x}\:=\:\mathrm{sin}\:^{\mathrm{2}} \theta\:\rightarrow{dx}=\mathrm{2sin}\:\theta\:\mathrm{cos}\:\theta\:{d}\theta…
Question Number 52999 by Tawa1 last updated on 16/Jan/19 $$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{1}}\:\:\boldsymbol{\mathrm{dx}}\:\:\: \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 16/Jan/19 $${tough}\:{question}…{wait}… \\…