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Author: Tinku Tara

1-calculate-dx-x-1-3-x-2-3-2-decompose-the-fraction-F-x-1-x-1-3-x-2-3-

Question Number 86983 by mathmax by abdo last updated on 01/Apr/20 $$\left.\mathrm{1}\right)\:{calculate}\:\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)^{\mathrm{3}} } \\ $$ Commented by hknkrc46 last updated…

1-2x-2-3x-8-dx-

Question Number 152513 by ZiYangLee last updated on 29/Aug/21 $$\int\:\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{8}}\:{dx}\:=? \\ $$ Commented by alisiao last updated on 29/Aug/21 $$ \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:\int\:\frac{{dx}}{\left({x}+\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} +\frac{\mathrm{55}}{\mathrm{16}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\int\:\:\frac{{dt}}{{t}^{\mathrm{2}} +\frac{\mathrm{55}}{\mathrm{16}}}\:…

Find-in-terms-of-using-the-equations-i-u-2-sin-2-2gd-cos-ii-t-u-cos-g-sin-iii-d-ut-sin-gt-2-sin-2-

Question Number 21441 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Find}\:\alpha\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\theta\:\mathrm{using}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\left({i}\right)\:{u}^{\mathrm{2}} \:\mathrm{sin}^{\mathrm{2}} \:\alpha\:=\:\mathrm{2}{gd}\:\mathrm{cos}\:\theta \\ $$$$\left({ii}\right)\:{t}\:=\:\frac{{u}\:\mathrm{cos}\:\alpha}{{g}\:\mathrm{sin}\:\theta} \\ $$$$\left({iii}\right)\:−{d}\:=\:{ut}\:\mathrm{sin}\:\alpha\:−\:\frac{{gt}^{\mathrm{2}} \:\mathrm{sin}\:\theta}{\mathrm{2}} \\ $$ Answered by $@ty@m last…

In-any-ABC-a-b-cos-C-c-cos-B-

Question Number 21431 by Tinkutara last updated on 23/Sep/17 $$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:{a}\left({b}\:\mathrm{cos}\:{C}\:−\:{c}\:\mathrm{cos}\:{B}\right)\:= \\ $$ Answered by $@ty@m last updated on 23/Sep/17 $$={ab}\mathrm{cos}\:{C}−{ac}\mathrm{cos}\:{B} \\ $$$$=\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}}−\frac{{c}^{\mathrm{2}}…

In-any-ABC-the-value-of-2ac-sin-A-B-C-2-is-

Question Number 21430 by Tinkutara last updated on 23/Sep/17 $$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{2}{ac}\:\mathrm{sin}\:\left(\frac{{A}\:−\:{B}\:+\:{C}}{\mathrm{2}}\right)\:\mathrm{is} \\ $$ Answered by $@ty@m last updated on 23/Sep/17 $$=\mathrm{2}{ac}\mathrm{sin}\:\left(\frac{\pi−\mathrm{2}{B}}{\mathrm{2}}\right) \\ $$$$=\mathrm{2}{ac}\mathrm{cos}\:{B} \\…