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Category: Integration

pi-pi-sin-1-1-x-2-dx-

Question Number 60881 by aliesam last updated on 26/May/19 $$\underset{−\pi} {\overset{\pi} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Commented by MJS last updated on 26/May/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this},\:\mathrm{not}\:\mathrm{even} \\ $$$$\mathrm{approximate}.\:\mathrm{it}'\mathrm{s}\:\mathrm{undefined}\:\mathrm{at}\:{x}=\pm\mathrm{1}\:\mathrm{and}…

Question-191921

Question Number 191921 by Rupesh123 last updated on 03/May/23 Answered by AST last updated on 03/May/23 $$\int\left(\mathrm{3}{x}+\mathrm{5}\right){dx}=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{5}{x}+{c} \\ $$$$\int_{−\mathrm{4}} ^{\mathrm{2}} \left(\mathrm{3}{x}+\mathrm{5}\right){dx}=\left(\mathrm{16}+{c}\right)−\left(\mathrm{4}+{c}\right)=\mathrm{12} \\ $$$$\Rightarrow\left(\mathrm{4}+{log}_{\mathrm{3}} {x}\right)\left({log}_{\mathrm{3}}…

tan-x-x-dx-

Question Number 126369 by I want to learn more last updated on 19/Dec/20 $$\int\:\frac{\mathrm{tan}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\mathrm{dx} \\ $$ Answered by Olaf last updated on 20/Dec/20 $$\mathrm{I}\:\mathrm{believe}\:\mathrm{the}\:\mathrm{only}\:\mathrm{way}\:\mathrm{to}\:\mathrm{handle}\:\mathrm{this} \\…

nice-calculus-calculate-0-e-t-t-2-j-0-t-dt-where-j-v-x-x-v-n-0-1-n-x-2n-2-2n

Question Number 126349 by mnjuly1970 last updated on 19/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{calculate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\overset{???} {=}\int_{\mathrm{0}} ^{\:\:\infty} {e}^{\:−{t}} \:{t}^{\:\mathrm{2}} \:{j}_{\mathrm{0}} \left(\:{t}\:\right){dt} \\ $$$$\:\:\:\:\:{where}\::\:\:{j}_{\left({v}\right)} \left({x}\right)={x}^{{v}} \underset{{n}=\mathrm{0}} {\overset{\:\infty}…

e-w-w-n-1-dw-n-N-

Question Number 60797 by arcana last updated on 25/May/19 $$\int\frac{{e}^{{w}} }{{w}^{{n}+\mathrm{1}} }{dw},\:{n}\in\mathbb{N} \\ $$ Commented by MJS last updated on 26/May/19 $$\mathrm{this}\:\mathrm{reminds}\:\mathrm{me}\:\mathrm{of}\:\Gamma\left({x}\right)=\underset{\mathrm{0}} {\overset{\infty} {\int}}\mathrm{e}^{−{t}} {t}^{{x}−\mathrm{1}}…

advanced-calculus-prove-that-1-x-2-x-x-2-2-x-1-pi-cos-pix-2-

Question Number 126323 by mnjuly1970 last updated on 19/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:\:{that}\:::: \\ $$$$\:\:\:\:\:\frac{\Gamma\left(\frac{\mathrm{1}−{x}}{\mathrm{2}}\right)\Gamma\left({x}\right)}{\Gamma\left(\frac{{x}}{\mathrm{2}}\right)}\:\overset{???} {=}\:\frac{\mathrm{2}^{{x}−\mathrm{1}} \sqrt{\pi}}{{cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\ $$$$ \\ $$ Terms of Service Privacy Policy…