Question Number 155013 by amin96 last updated on 24/Sep/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(−{lnx}\right)\frac{{x}^{\mu−\mathrm{1}} }{\:\sqrt{−{ln}\left({x}\right)}}{dx}=? \\ $$ Answered by mnjuly1970 last updated on 24/Sep/21 $$\:\:\:−{ln}\left({x}\right)={t}^{\:\mathrm{2}} \:\Rightarrow\:{x}={e}^{\:−{t}^{\mathrm{2}} }…
Question Number 155016 by ArielVyny last updated on 24/Sep/21 $$\int_{\mathrm{0}} ^{\infty} {tan}^{\mathrm{2}} {u}\left(\mathrm{1}−\frac{\mathrm{1}}{\left({u}+\mathrm{1}\right)^{\mathrm{2}} }\right){du} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89425 by M±th+et£s last updated on 17/Apr/20 $$\int_{\mathrm{1}} ^{\mathrm{4}} \sqrt{\mathrm{1}+\left(\frac{{y}^{\mathrm{3}} }{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}{y}^{−\mathrm{1}} \right)^{\mathrm{2}} }\:{dy} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 154928 by qaz last updated on 23/Sep/21 $$\mathrm{Prove}::\:\:\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{m}} {\sum}}\begin{pmatrix}{\mathrm{m}}\\{\mathrm{k}}\end{pmatrix}^{\mathrm{2}} \begin{pmatrix}{\mathrm{n}+\mathrm{2m}−\mathrm{k}}\\{\:\:\:\:\:\:\mathrm{2m}}\end{pmatrix}=\begin{pmatrix}{\mathrm{m}+\mathrm{n}}\\{\:\:\:\:\mathrm{n}}\end{pmatrix}^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 154927 by physicstutes last updated on 23/Sep/21 $$\mathrm{Let}\:{I}_{{n}} =\int{x}^{{n}} {e}^{−{x}} {dx} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}^{{n}} {e}^{−{x}} {dx}={n}! \\ $$ Answered by…
Question Number 154926 by physicstutes last updated on 23/Sep/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{2}{x}^{\mathrm{2}} }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}= \\ $$ Answered by qaz last updated on 23/Sep/21 $$\int_{\mathrm{0}}…
Question Number 23849 by Sudipta Jana last updated on 08/Nov/17 $$\int\frac{{x}^{\mathrm{6}} +\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$ Answered by anunil1234 last updated on 08/Nov/17 $$\int\left(\mathrm{x}^{\mathrm{2}} \:+\frac{\left(−\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)}{\mathrm{x}^{\mathrm{4}}…
Question Number 89384 by nimnim last updated on 17/Apr/20 Commented by mathmax by abdo last updated on 17/Apr/20 $${let}\:{try}\:{another}\:{way}\:\:{we}\:{consider}\:{the}\:{diffeomorphism} \\ $$$$\left({u},{v}\right)\rightarrow\left({x},{y}\right)\:/{x}−{y}={u}\:{and}\:{x}+{y}\:={v}\:\Rightarrow{x}\:=\frac{{u}+{v}}{\mathrm{2}}\:{andy}=\frac{−{u}+{v}}{\mathrm{2}} \\ $$$$\Rightarrow\varphi\left({u},{v}\right)=\left(\varphi_{\mathrm{1}} \left({u},{v}\right),\varphi_{\mathrm{2}} \left({u},{v}\right)\right)=\left({x},{y}\right)=\left(\frac{{u}}{\mathrm{2}}+\frac{{v}}{\mathrm{2}},−\frac{{u}}{\mathrm{2}}+\frac{{v}}{\mathrm{2}}\right)…
Question Number 89382 by M±th+et£s last updated on 17/Apr/20 $$\int_{\mathrm{0}} ^{\infty} {e}^{−\mathrm{2}{x}} \:{cos}\left(\mathrm{3}{x}\right)\:{sin}\left(\mathrm{4}{x}\right) \\ $$ Commented by mathmax by abdo last updated on 17/Apr/20 $${cos}\left(\mathrm{3}{x}\right){sin}\left(\mathrm{4}{x}\right)\:={cos}\left(\mathrm{3}{x}\right){cos}\left(\frac{\pi}{\mathrm{2}}−\mathrm{4}{x}\right)…
Question Number 23830 by anunil1234 last updated on 07/Nov/17 $$\int\mathrm{sin}\left(\mathrm{101x}\right)\mathrm{sin}^{\mathrm{99}} \mathrm{xdx} \\ $$ Commented by prakash jain last updated on 07/Nov/17 $$\mathrm{sin}\:\left(\mathrm{100}{x}+{x}\right)\mathrm{sin}^{\mathrm{99}} {x} \\ $$$$=\mathrm{sin}\:\left(\mathrm{100}{x}\right)\mathrm{cos}\:{x}\mathrm{sin}^{\mathrm{99}}…