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Category: Integration

calculus-please-solve-1-0-pi-4-tan-x-cot-x-dx-2-0-pi-4-tan-x-ln-1-tan-2-x-dx-M-N-july-1970-Good-luck-

Question Number 110888 by mnjuly1970 last updated on 31/Aug/20 $$\:\:\:\:\:\:\:\:\:\:….{calculus}…. \\ $$$${please}\:{solve}\:: \\ $$$$ \\ $$$$\Omega_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \left(\sqrt{{tan}\left({x}\right)}\:+\sqrt{{cot}\left({x}\right)}\:\right){dx}=?? \\ $$$$\:\Omega_{\mathrm{2}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {tan}\left({x}\right){ln}\left(\left(\mathrm{1}+{tan}^{\mathrm{2}} \left({x}\right)\right)\right){dx}\:=??…

Question-45352

Question Number 45352 by Meritguide1234 last updated on 12/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 12/Oct/18 $${x}−{y}=\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} } \\ $$$${y}\left(\frac{{x}}{{y}}−\mathrm{1}\right)=\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:\:\:\:\:\:\:{t}=\frac{{x}}{{y}} \\ $$$${y}\left({t}−\mathrm{1}\right)={t}^{\mathrm{2}}…

1-e-e-e-ln-x-ln-ln-x-x-dx-2-lim-x-pi-4-cosec-2-x-2-cot-x-1-3-Given-xy-16y-9x-45-4-x-3-y-5-find-9-xy-

Question Number 110875 by bemath last updated on 31/Aug/20 $$\left(\mathrm{1}\right)\underset{\mathrm{e}} {\overset{\mathrm{e}^{\mathrm{e}} } {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{x}\right).\mathrm{ln}\:\left(\mathrm{ln}\:\left(\mathrm{x}\right)\right)}{\mathrm{x}}\:\mathrm{dx}\:? \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\:\frac{\mathrm{cosec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2}}{\mathrm{cot}\:\mathrm{x}−\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Given}\:\begin{cases}{\mathrm{xy}=\frac{\mathrm{16y}−\mathrm{9x}}{\mathrm{45}}}\\{\frac{\mathrm{4}}{\:\sqrt{\mathrm{x}}}−\frac{\mathrm{3}}{\:\sqrt{\mathrm{y}}}\:=\:\mathrm{5}}\end{cases} \\ $$$$\Rightarrow\mathrm{find}\:\mathrm{9}\sqrt{\mathrm{xy}} \\ $$ Answered by…

Question-45334

Question Number 45334 by Meritguide1234 last updated on 12/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 12/Oct/18 $${using}\:{gamma}\:{beta}\:{function} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{{m}−\mathrm{1}} \left(\mathrm{1}−{t}\right)^{{n}−\mathrm{1}} {dt}=\beta\left({m},{n}\right)=\frac{\lceil\left({m}\right)\lceil\left({n}\right)}{\lceil\left({m}+{n}\right)} \\ $$$$\lceil\left({n}+\mathrm{1}\right)={n}!…

lim-n-1-r-1-n-1-3-r-r-k-1-r-2k-1-

Question Number 110772 by Dwaipayan Shikari last updated on 30/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{3}^{{r}} {r}!}\underset{{k}=\mathrm{1}} {\overset{{r}} {\prod}}\left(\mathrm{2}{k}−\mathrm{1}\right)\right) \\ $$ Terms of Service Privacy Policy Contact:…

let-a-lt-1-and-f-a-0-1-ln-x-ln-1-ax-dx-1-find-a-explicit-form-of-f-a-2-calculate-g-a-0-1-xln-x-1-ax-dx-3-calculate-0-1-ln-x-ln-2-x-dx-4-calculate-0-1-xln-x-2-x-

Question Number 45235 by maxmathsup by imad last updated on 10/Oct/18 $${let}\:\mid{a}\mid<\mathrm{1}\:{and}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{ax}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xln}\left({x}\right)}{\mathrm{1}+{ax}}{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{2}+{x}\right){dx} \\…