Question Number 177241 by peter frank last updated on 02/Oct/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{a}\right)}\mathrm{dx} \\ $$ Answered by cortano1 last updated on 02/Oct/22 $$\:\Rightarrow\mathrm{x}−\mathrm{a}=\mathrm{y}\:;\:\Rightarrow\mathrm{dx}=\mathrm{dy} \\ $$$$\mathrm{C}=\int\:\frac{\mathrm{sin}\:\left(\mathrm{a}+\mathrm{y}\right)}{\mathrm{sin}\:\mathrm{y}}\:\mathrm{dy}=\int\left(\:\mathrm{cos}\:\mathrm{a}+\mathrm{sin}\:\mathrm{a}\:\frac{\mathrm{cos}\:\mathrm{y}}{\mathrm{sin}\:\mathrm{y}}\right)\mathrm{dy} \\ $$$$\mathrm{C}=\:\left(\mathrm{x}−\mathrm{a}\right)\mathrm{cos}\:\mathrm{a}+\mathrm{sin}\:\mathrm{a}\:\int\:\frac{\mathrm{d}\left(\mathrm{sin}\:\mathrm{y}\right)}{\mathrm{sin}\:\mathrm{y}}\:…
Question Number 46171 by math khazana by abdo last updated on 22/Oct/18 $${find}\:\int\:\:\:\:\frac{{dx}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}+\mathrm{2}}} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 22/Oct/18 $${excellent}\:{problem}… \\ $$…
Question Number 177242 by peter frank last updated on 02/Oct/22 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{3x}^{\mathrm{16}} +\mathrm{5x}^{\mathrm{14}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{4}} }\mathrm{dx} \\ $$$$ \\ $$ Answered by som(math1967)…
Question Number 46156 by Meritguide1234 last updated on 21/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 21/Oct/18 $${x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1} \\ $$$$={x}^{\mathrm{2}} \left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{2}{x}+\frac{\mathrm{2}}{{x}}−\mathrm{1}\right)…
Question Number 46129 by Necxx last updated on 21/Oct/18 Commented by Meritguide1234 last updated on 21/Oct/18 $${put}\:{x}={tan}\theta \\ $$$$\int_{\mathrm{0}} ^{\pi/\mathrm{4}} {log}\left(\mathrm{1}+{tan}\theta\right){d}\theta \\ $$$${use}\:{f}\left({a}−{x}\right)\rightarrow{f}\left({x}\right) \\ $$$${I}=\frac{\pi}{\mathrm{8}}{log}\mathrm{2}…
Question Number 177194 by peter frank last updated on 02/Oct/22 $$\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{14}}{\mathrm{9}}} \left(\mathrm{cos}\:\mathrm{x}\right)^{\frac{\mathrm{4}}{\mathrm{9}}} } \\ $$ Answered by som(math1967) last updated on 02/Oct/22 $$\int\frac{{sec}^{\mathrm{2}} {xdx}}{\left({sinx}\right)^{\frac{\mathrm{14}}{\mathrm{9}}} ×\left({cosx}\right)^{\frac{\mathrm{4}}{\mathrm{9}}}…
Question Number 46103 by rahul 19 last updated on 21/Oct/18 $${Find}\:{the}\:{area}\:{enclosed}\:{between}\:{curves} \\ $$$${y}^{\mathrm{2}} \left(\mathrm{2}{a}−{x}\right)={x}^{\mathrm{3}} \:{and}\:{line}\:{x}=\mathrm{2}\:{above}\:{the} \\ $$$${x}−{axis}\:? \\ $$$${Graphing}\:{calculators}\:{are}\:{not}\:{allowed}.. \\ $$ Commented by rahul 19…
Question Number 46101 by Saorey last updated on 21/Oct/18 $$\mathrm{I}=\int\frac{\mathrm{x}^{\mathrm{n}+\mathrm{1}} }{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{n}} }}\mathrm{dx}=? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 21/Oct/18 $${x}^{{n}} ={tan}^{\mathrm{2}} \theta\:\:\:\:{so}\:{nx}^{{n}−\mathrm{1}} {dx}=\mathrm{2}{tan}\theta{sec}^{\mathrm{2}}…
Question Number 46091 by sandeepkeshari0797@gmail.com last updated on 21/Oct/18 Commented by maxmathsup by imad last updated on 21/Oct/18 $${let}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{{u}} \:\frac{{sinx}}{{x}}{e}^{−{tx}} {dx}\:\:{with}\:{t}\geqslant{o}\:\:{we}\:{have}\:{f}^{'} \left({t}\right)=−\int_{\mathrm{0}} ^{{u}} \:{sinx}\:{e}^{−{tx}}…
Question Number 46087 by Saorey last updated on 21/Oct/18 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}!! \\ $$$$\mathrm{calculate}: \\ $$$$\mathrm{I}=\underset{\mathrm{2}} {\overset{\mathrm{1}+\mathrm{e}^{\mathrm{2}} } {\int}}\frac{\mathrm{12288ln}\left(\mathrm{x}−\mathrm{1}\right)}{\left[\mathrm{ln}^{\mathrm{12}} \left(\mathrm{x}−\mathrm{1}\right)+\mathrm{4096}\right]\left(\mathrm{x}−\mathrm{1}\right)}\mathrm{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{thanks}!!! \\ $$ Answered by tanmay.chaudhury50@gmail.com…