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Question Number 151893 by peter frank last updated on 24/Aug/21

           ∫x(x^3 +a^3 )dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\int\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{a}^{\mathrm{3}} \right)\mathrm{dx} \\ $$

Answered by puissant last updated on 24/Aug/21

=∫x^4 +a^3 xdx  =(1/5)x^5 +(a^3 /2)x^2 +C..

$$=\int{x}^{\mathrm{4}} +{a}^{\mathrm{3}} {xdx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{5}}{x}^{\mathrm{5}} +\frac{{a}^{\mathrm{3}} }{\mathrm{2}}{x}^{\mathrm{2}} +{C}.. \\ $$

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