Question Number 214568 by Ikbal last updated on 12/Dec/24 $$\int\frac{{b}+{ax}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx} \\ $$ Answered by MathematicalUser2357 last updated on 18/Dec/24 $$\int\frac{{ax}+{b}}{\mathrm{sin}\:{x}+\mathrm{1}}{dx} \\ $$$$=\int\frac{\left({ax}+{b}\right)\mathrm{sec}\:{x}}{\mathrm{tan}\:{x}+\mathrm{sec}\:{x}}{dx} \\ $$$$=−\frac{{ax}+{b}}{\mathrm{tan}\:{x}+\mathrm{sec}\:{x}}+\int\frac{{a}}{\mathrm{tan}\:{x}+\mathrm{sec}\:{x}}{dx} \\…
Question Number 214560 by ajfour last updated on 12/Dec/24 $$\int_{\mathrm{1}} ^{\:\:{x}} \frac{\mathrm{ln}\:{x}}{\:\sqrt{\mathrm{1}−\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} }}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 18/Dec/24 $$\:\cancel{\lesseqgtr} \\ $$…
Question Number 214509 by depressiveshrek last updated on 10/Dec/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid}\:\mathrm{of}\:\mathrm{revolution} \\ $$$$\mathrm{generated}\:\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded} \\ $$$$\mathrm{by}\:{y}={x}\left(\mathrm{2}−{x}\right)\:\mathrm{and}\:{y}={x}\:\mathrm{about}\:\mathrm{the}\:\mathrm{y}−\mathrm{axis}. \\ $$ Commented by mr W last updated on 11/Dec/24 $${you}\:{seem}\:{never}\:{to}\:{give}\:{any}\:{feedback}…
Question Number 214498 by universe last updated on 10/Dec/24 Answered by mr W last updated on 10/Dec/24 $$=\mathrm{4}\pi\int_{\mathrm{0}} ^{\infty} {re}^{−{r}^{\mathrm{2}} } {r}^{\mathrm{2}} {dr} \\ $$$$=\mathrm{2}\pi\int_{\mathrm{0}}…
Question Number 214360 by shunmisaki007 last updated on 06/Dec/24 $$\mathrm{Find}\:\underset{−\infty} {\overset{\infty} {\int}}{e}^{−{ax}^{\mathrm{2}} } {dx}\:\mathrm{when}\:{a}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{without}\:\mathrm{changing}\:\mathrm{the}\:\mathrm{coordinate}. \\ $$ Answered by mathmax last updated on 06/Dec/24 $$=\mathrm{2}\int_{\mathrm{0}} ^{\infty}…
Question Number 214301 by efronzo1 last updated on 04/Dec/24 $$\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{sin}\:\mathrm{x}\right)+\:\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{dx}\:=? \\ $$ Commented by Frix last updated on 04/Dec/24 $$\mathrm{Should}\:\mathrm{be}\:\frac{\pi}{\mathrm{2}} \\…
Question Number 213944 by Spillover last updated on 22/Nov/24 Answered by Spillover last updated on 23/Nov/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 213962 by depressiveshrek last updated on 22/Nov/24 $$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}\left({x}^{\mathrm{4}} −\mathrm{5}\right)\left({x}^{\mathrm{5}} −\mathrm{5}{x}+\mathrm{1}\right)}{dx} \\ $$ Answered by Frix last updated on 23/Nov/24 $$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}\left({x}^{\mathrm{4}} −\mathrm{5}\right)\left({x}^{\mathrm{5}}…
Question Number 213945 by Spillover last updated on 22/Nov/24 Answered by mathmax last updated on 23/Nov/24 $${I}=\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left[{x}\right]\left(\mathrm{1}+{x}−\left[{x}\right]\right)} {dx} \\ $$$$=\mathrm{1}+\sum_{{n}=\mathrm{1}} ^{\infty} \int_{{n}} ^{{n}+\mathrm{1}}…
Question Number 213934 by ajfour last updated on 22/Nov/24 $$\int_{−\pi/\mathrm{2}} ^{\:\pi/\mathrm{2}} \int_{\mathrm{0}} ^{\:{R}} \frac{\left({d}\theta\right)\left({dr}\right)\left({a}+{r}\mathrm{cos}\:\theta\right)}{\left({r}^{\mathrm{2}} +{a}^{\mathrm{2}} +\mathrm{2}{ar}\mathrm{cos}\:\theta\right)^{\mathrm{3}/\mathrm{2}} }\:={f}\left({a},{R}\right) \\ $$$${Find}\:{f}\left({a},\:{R}\right). \\ $$ Commented by ajfour last…