Question Number 91271 by mathmax by abdo last updated on 29/Apr/20 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 91270 by mathmax by abdo last updated on 29/Apr/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 91269 by mathmax by abdo last updated on 29/Apr/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{2}\right)^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 156779 by Fresnel last updated on 15/Oct/21 $$\int\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$ Answered by phanphuoc last updated on 15/Oct/21 $${x}={tant} \\ $$ Answered…
Question Number 156775 by mnjuly1970 last updated on 15/Oct/21 $$ \\ $$$$\:\:\:{f}\:\:{is}\:\:{a}\:{function}\:{that}\:{assigns} \\ $$$$\:\:\:{to}\:{each}\:{natural}\:{number}\: \\ $$$$\:\:\:\:\:{multiplication}\:{of}\:{its}\:{digits}\: \\ $$$$\:\:\:\:{for}\:{exampl}\::\:\:{f}\left(\:\mathrm{200}\right)=\mathrm{0} \\ $$$$\:\:\:\:{f}\:\left(\:\mathrm{128}\:\right)=\mathrm{1}×\mathrm{2}×\mathrm{8}\:=\mathrm{16} \\ $$$$\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:: \\ $$$$\:\:\:\:\:{f}\:\left(\mathrm{100}\right)\:+\:{f}\left(\mathrm{101}\:\right)+\:{f}\:\left(\mathrm{102}\:\right)+…{f}\left(\mathrm{999}\right)=? \\…
Question Number 91223 by M±th+et+s last updated on 28/Apr/20 $${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