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Category: Integration

Question-203747

Question Number 203747 by patrice last updated on 27/Jan/24 Answered by esmaeil last updated on 27/Jan/24 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}}{\mathrm{1}+{cosx}}{dx}+\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sinx}}{\mathrm{1}+{cosx}}{dx} \\ $$$${x}={u}\rightarrow{dx}={du} \\ $$$$\frac{{dx}}{\mathrm{1}+{cosx}}={dv}\rightarrow{v}={tan}\frac{{x}}{\mathrm{2}}…

Question-203385

Question Number 203385 by patrice last updated on 18/Jan/24 Answered by Mathspace last updated on 18/Jan/24 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:\Rightarrow{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{3}{n}}…

Question-202930

Question Number 202930 by Calculusboy last updated on 06/Jan/24 Answered by MathematicalUser2357 last updated on 06/Jan/24 $$\mathrm{No}\:\mathrm{antiderivative}\:\mathrm{could}\:\mathrm{be}\:\mathrm{found}\:\mathrm{within}\:\mathrm{the}\:\mathrm{given} \\ $$$$\mathrm{time}\:\mathrm{limit},\:\mathrm{or}\:\mathrm{all}\:\mathrm{supported}\:\mathrm{integration}\:\mathrm{methods} \\ $$$$\mathrm{were}\:\mathrm{tried}\:\mathrm{unsuccessfully}.\:\mathrm{Note}\:\mathrm{that}\:\mathrm{many}\:\mathrm{functions} \\ $$$$\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{an}\:\mathrm{elementary}\:\mathrm{antiderivative}. \\ $$…