Category: Integration

Question Number 63615 by aliesam last updated on 06/Jul/19 Commented by mathmax by abdo last updated on 06/Jul/19 $${changement}\:\:{x}=−{t}\:\:{give}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:{xln}\left(\mathrm{1}+\mathrm{10}^{{x}} \right){dx}\:=−\int_{−\mathrm{1}} ^{\mathrm{1}} \:\left(−{t}\right){ln}\left(\mathrm{1}+\mathrm{10}^{−{t}} \right)\left(−{dt}\right)…

Question Number 63570 by mr W last updated on 05/Jul/19 Commented by mathmax by abdo last updated on 05/Jul/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{{x}} {dx}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{{i}\pi{x}}…

Question Number 129068 by bagjagunawan last updated on 12/Jan/21 Answered by mnjuly1970 last updated on 12/Jan/21 $$ans::\pi ln(1-e^{-\pi n})\dots .$$ Terms of Service Privacy Policy…

Question Number 129060 by benjo_mathlover last updated on 12/Jan/21 $$\varphi =\int \frac{\ln \left(\mathrm{x}\right)}{{\mathrm{x}}^2}\mathrm{dx}$$ Answered by liberty last updated on 12/Jan/21 $$\mathrm{let}\ln \left(\mathrm{x}\right)=\mathrm{h}\Rightarrow \mathrm{x}={\mathrm{e}}^{\mathrm{h}}$$$$\:\phi\:=\:\int\:\frac{\mathrm{h}}{\mathrm{e}^{\mathrm{2h}} }\:\left(\mathrm{e}^{\mathrm{h}} \:\mathrm{dh}\:\right)=\:\int\:\mathrm{h}.\mathrm{e}^{−\mathrm{h}}…

Question Number 129057 by pipin last updated on 12/Jan/21 $$$$$${\int }_1^{\mathrm{\infty }}\frac{1}{1+{\mathrm{x}}^3}\mathrm{dx}=\dots$$ Answered by MJS_new last updated on 12/Jan/21 $$\int\frac{{dx}}{{x}^{\mathrm{3}}…