Question Number 218003 by hardmath last updated on 25/Mar/25
$$\mathrm{1}.\:\:\:\int\:\:\frac{\mathrm{x}\:\mathrm{dx}}{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{4}\right)} \\ $$$$\mathrm{2}.\:\:\:\int\:\:\frac{\mathrm{x}\:+\:\mathrm{2}}{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{2x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$$$\mathrm{3}.\:\:\:\int\:\:\frac{\mathrm{2x}\:+\:\mathrm{7}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}}\:\mathrm{dx} \\ $$
Commented by Ghisom last updated on 25/Mar/25
$$\mathrm{these}\:\mathrm{are}\:\mathrm{rather}\:\mathrm{Easymath}… \\ $$$$\mathrm{1}.\:\:\:\:\:=\int\left(\frac{\mathrm{2}}{{x}+\mathrm{4}}−\frac{\mathrm{1}}{{x}+\mathrm{2}}\right){dx} \\ $$$$\mathrm{2}.\:\:\:\:\:=\int\left(\frac{\mathrm{1}}{{x}−\mathrm{2}}−\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){dx} \\ $$$$\mathrm{3}.\:\:\:\:\:=\int\left(\frac{\mathrm{13}}{\mathrm{2}\left({x}−\mathrm{3}\right)}−\frac{\mathrm{9}}{\mathrm{2}\left({x}−\mathrm{1}\right)}\right){dx} \\ $$
Commented by mnjuly1970 last updated on 25/Mar/25
$${gibarchakanat}\:{sir}\:{hardmath}. \\ $$
Commented by hardmath last updated on 25/Mar/25
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Commented by mnjuly1970 last updated on 25/Mar/25
$$\:{your}\:\:{questions}\:{are}\:{usually} \\ $$$$\:\:{hard}\:{but}\:{nice}.{particularly}\:{trigonometric} \\ $$$${with}\:{geometric}\:\:{inequalities}. \\ $$
Commented by hardmath last updated on 25/Mar/25
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$
Commented by mnjuly1970 last updated on 25/Mar/25
$$\:\cancel{\lesseqgtr} \\ $$