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Question Number 147943 by mathdanisur last updated on 24/Jul/21

∫ (((x^2  + x)^2 )/(x + 1)) = ?

$$\int\:\frac{\left({x}^{\mathrm{2}} \:+\:{x}\right)^{\mathrm{2}} }{{x}\:+\:\mathrm{1}}\:=\:? \\ $$

Commented bytabata last updated on 24/Jul/21

=∫ ((x^2 (x+1)^2 )/((x+1)))dx=∫ x^2 (x+1)dx=(x^4 /4)+(x^3 /3)+C    ⟨M.T⟩

$$=\int\:\frac{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{2}} }{\left({x}+\mathrm{1}\right)}{dx}=\int\:{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right){dx}=\frac{{x}^{\mathrm{4}} }{\mathrm{4}}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}}+{C} \\ $$ $$ \\ $$ $$\langle{M}.{T}\rangle \\ $$

Commented bymathdanisur last updated on 24/Jul/21

Thank you Ser

$${Thank}\:{you}\:{Ser} \\ $$

Commented bytabata last updated on 25/Jul/21

you are welcome

$${you}\:{are}\:{welcome} \\ $$

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