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Category: Integration

dx-csc-x-cos-x-

Question Number 175602 by cortano1 last updated on 03/Sep/22 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{csc}\:\mathrm{x}+\:\mathrm{cos}\:\mathrm{x}}\:=? \\ $$ Commented by infinityaction last updated on 04/Sep/22 $$\:\:\int\frac{\mathrm{2}\boldsymbol{\mathrm{sin}{x}}\:}{\mathrm{2}+\mathrm{2}\boldsymbol{\mathrm{sin}{x}}.\boldsymbol{\mathrm{cos}{x}}\:}\boldsymbol{{dx}} \\ $$$${I}\:=\underset{\Psi} {\int}\frac{\left(\boldsymbol{\mathrm{sin}{x}}+\boldsymbol{\mathrm{cos}{x}}\right)\:\:\boldsymbol{{dx}}}{\:\:\mathrm{3}−\left(\boldsymbol{\mathrm{sin}{x}}−\boldsymbol{\mathrm{cos}{x}}\right)^{\mathrm{2}} \:\:}+\int_{\Phi} \frac{\left(\boldsymbol{\mathrm{sin}{x}}\:−\boldsymbol{\mathrm{cos}{x}}\right)\:\boldsymbol{{dx}}}{\mathrm{1}+\left(\boldsymbol{\mathrm{sin}{x}}+\boldsymbol{\mathrm{cos}{x}}\right)^{\mathrm{2}}…

let-g-x-0-t-ln-t-dt-1-xt-3-with-x-gt-0-1-give-a-explicit-form-of-g-x-2-calculate-0-t-ln-t-1-t-3-dt-3-calculate-0-tln-t-1-2t-3-dt-4-calculate-A-

Question Number 44515 by maxmathsup by imad last updated on 30/Sep/18 $${let}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}\:{ln}\left({t}\right){dt}}{\left(\mathrm{1}+{xt}\right)^{\mathrm{3}} }\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{a}\:{explicit}\:{form}\:{of}\:{g}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}\:{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)^{\mathrm{3}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty}…

prove-that-2-ln-x-dx-x-2-ln-x-ln-xe-C-

Question Number 44512 by arvinddayama01@gmail.com last updated on 30/Sep/18 $$\boldsymbol{{prove}}\:\boldsymbol{{that}}:−\int\mathrm{2}^{\boldsymbol{\mathrm{ln}}\:\boldsymbol{\mathrm{x}}} \:\boldsymbol{\mathrm{dx}}\:=\:\frac{\boldsymbol{\mathrm{x}}.\mathrm{2}^{\boldsymbol{\mathrm{ln}}\:\boldsymbol{\mathrm{x}}} }{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{xe}}\right)}\:+\boldsymbol{\mathrm{C}} \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated on 30/Sep/18…

tan-x-dx-

Question Number 44509 by arvinddayama01@gmail.com last updated on 30/Sep/18 $$\int\sqrt{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\mathrm{x}}}\:\:\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by maxmathsup by imad last updated on 30/Sep/18 $${this}\:{integral}\:{is}\:{solved}\:\:{look}\:\:{at}\:{the}\:{platform}\:… \\ $$ Answered…

sin-x-dx-

Question Number 44508 by arvinddayama01@gmail.com last updated on 30/Sep/18 $$\int\sqrt{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\:}\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by MJS last updated on 01/Oct/18 $$\mathrm{please}\:\mathrm{go}\:\mathrm{to}\:\mathrm{question}\:\mathrm{42945}\:\mathrm{and}\:\mathrm{read}\:\mathrm{all}\:\mathrm{the} \\ $$$$\mathrm{answers}\:\mathrm{and}\:\mathrm{comments}.\:\mathrm{the}\:\mathrm{solution}\:\mathrm{is}\:\mathrm{there} \\ $$ Answered…

Question-44498

Question Number 44498 by peter frank last updated on 30/Sep/18 Commented by maxmathsup by imad last updated on 30/Sep/18 $${changement}\:\mathrm{4}^{{x}} ={t}\:{give}\:\:{e}^{{xln}\left(\mathrm{4}\right)} ={t}\:\Rightarrow{xln}\left(\mathrm{4}\right)={ln}\left({t}\right)\:\Rightarrow{dx}=\frac{\mathrm{1}}{{tln}\left(\mathrm{4}\right)}{dt} \\ $$$${I}\:=\:\int\mathrm{4}^{\mathrm{4}^{{t}} }…

Question-175553

Question Number 175553 by BHOOPENDRA last updated on 02/Sep/22 Answered by Frix last updated on 03/Sep/22 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{\left({x}^{{n}} −\mathrm{1}\right)\left({x}−\mathrm{1}\right)}{{x}^{{n}+\mathrm{3}} −\mathrm{1}}{dx}\overset{\left(\mathrm{let}\:{t}=\frac{\mathrm{1}}{{x}}\right)} {=}\underset{\infty} {\overset{\mathrm{1}} {\int}}\frac{\left({t}^{{n}} −\mathrm{1}\right)\left({t}−\mathrm{1}\right)}{{t}^{{n}+\mathrm{3}}…