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Category: Integration

dx-x-x-2018-1-

Question Number 35456 by math1967 last updated on 19/May/18 $$\int\frac{{dx}}{{x}\left({x}^{\mathrm{2018}} +\mathrm{1}\right)} \\ $$ Answered by ajfour last updated on 19/May/18 $${I}=−\frac{\mathrm{1}}{\mathrm{2018}}\int\:\frac{−\mathrm{2018}{x}^{−\mathrm{19}} {dx}}{\mathrm{1}+{x}^{−\mathrm{2018}} } \\ $$$$\:\:=−\frac{\mathrm{1}}{\mathrm{2018}}\mathrm{ln}\:\mid\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2018}}…

let-m-gt-0-and-0-lt-a-lt-b-1-calculate-0-cos-mx-x-2-a-2-x-2-b-2-dx-2-find-the-value-of-0-cos-2x-x-2-1-x-2-3-dx-

Question Number 35438 by prof Abdo imad last updated on 19/May/18 $${let}\:{m}>\mathrm{0}\:{and}\:\mathrm{0}<{a}<{b}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{cos}\left({mx}\right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}}…

find-x-3-x-2-x-1-dx-

Question Number 35428 by abdo.msup.com last updated on 18/May/18 $${find}\:\:\:\:\:\int\:\:\:\:\frac{{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}\:−\mathrm{1}}}{dx} \\ $$ Commented by prof Abdo imad last updated on 19/May/18 $${let}\:{put}\:\:{I}\:\:=\:\int\:\:\:\:\:\:\frac{{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}−\mathrm{1}}}{dx} \\…