Question Number 91223 by M±th+et+s last updated on 28/Apr/20 $${what}\:{is}\:{complementary}\:{error}\:{function} \\ $$$${erfc}\left({t}\right)? \\ $$ Answered by MJS last updated on 28/Apr/20 $$\mathrm{erf}\:{x}\:=\frac{\mathrm{2}}{\:\sqrt{\pi}}\underset{\mathrm{0}} {\overset{{x}} {\int}}\mathrm{e}^{−{t}^{\mathrm{2}} }…
Question Number 156761 by gsk2684 last updated on 15/Oct/21 $${prove}\:{that} \\ $$$$\int\frac{{a}\:+\:{b}\:\mathrm{sin}\:{x}}{\left({b}\:+\:{a}\:\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{dx}=\frac{−\mathrm{cos}\:{x}}{{b}\:+\:{a}\:\mathrm{sin}\:{x}} \\ $$ Answered by cortano last updated on 15/Oct/21 $$\:\frac{\mathrm{d}}{\mathrm{dx}}\int\frac{\mathrm{a}+\mathrm{bsin}\:\mathrm{x}}{\left(\mathrm{b}+\mathrm{asin}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}=\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{−\mathrm{cos}\:\mathrm{x}}{\mathrm{b}+\mathrm{asin}\:\mathrm{x}}\right) \\…
Question Number 91220 by Ar Brandon last updated on 28/Apr/20 $$\int_{\mathrm{1}} ^{\mathrm{x}} \frac{\mathrm{lnt}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\mathrm{dt} \\ $$ Commented by abdomathmax last updated on 28/Apr/20 $${let}\:{take}\:{a}\:{try}\:\: \\…
Question Number 25682 by abdo imad last updated on 13/Dec/17 $${we}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:{t}^{{a}−\mathrm{1}} \left(\mathrm{1}\:+\:{t}\right)^{−\mathrm{1}} {dt}\:=\pi\:\left({sin}\left(\pi{a}\right)\right)^{−\mathrm{1}} \:{with}\:\mathrm{0}<{a}<\mathrm{1}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}\:+{x}^{\mathrm{16}} \right)^{−\mathrm{1}} {dx} \\ $$ Answered by ajfour…
Question Number 25683 by abdo imad last updated on 13/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{{n}} \:\right)\left(\:\mathrm{1}\:+\:{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 91217 by mhmd last updated on 28/Apr/20 Commented by Prithwish Sen 1 last updated on 28/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{n}\pi} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\boldsymbol{\mathrm{n}}\int_{\mathrm{0}} ^{\boldsymbol{\pi}} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\mathrm{n}\left[\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{\mathrm{cosxdx}}+\int_{\frac{\boldsymbol{\pi}}{\mathrm{2}}}…
Question Number 25676 by abdo imad last updated on 12/Dec/17 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\boldsymbol{{sin}}\left(\hat {\boldsymbol{{x}}}{n}\:\right)/\hat {{x}}\mathrm{2}\:+\:\mathrm{1}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 25677 by abdo imad last updated on 12/Dec/17 $${let}\:\mathrm{0}<{x}<\mathrm{1}\:\:{find}\:{the}\:{value}\:{of}\:{F}\left({x}\right)\:=\:\int\:\mathrm{ln}\:\left(\mathrm{1}+{x}\:{cost}\right){dt}\:{fromt}=\mathrm{0}\:{to}\:{t}={pi} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156743 by cortano last updated on 15/Oct/21 Answered by MJS_new last updated on 15/Oct/21 $$\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow \\ $$$$\int\frac{{dx}}{\:\sqrt[{\mathrm{4}}]{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{6}} }}= \\ $$$$=\int\frac{{dx}}{\:\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}= \\…
Question Number 156739 by cortano last updated on 15/Oct/21 Commented by john_santu last updated on 15/Oct/21 $$\:{B}=\int\:\sqrt{\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}}\:{dx} \\ $$$$\:\:\:=\int\:\sqrt{\frac{\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}{−\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}}\:{dx} \\ $$$$\:\:=\int\:\sqrt{−\mathrm{tan}\:\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}\:{dx} \\ $$$$\:\:=\int\sqrt{\mathrm{cot}\:\left({x}+\frac{\mathrm{3}\pi}{\mathrm{4}}\right)}\:{d}\left({x}+\frac{\mathrm{3}\pi}{\mathrm{4}}\right) \\ $$$$\:=\int\:\frac{{dq}}{\:\sqrt{\mathrm{tan}\:{q}}}\:…