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Prove-that-e-x-x-4-2-1-x-2-5-2-dx-e-x-1-x-2-x-1-x-2-3-2-C-




Question Number 124421 by Ar Brandon last updated on 03/Dec/20
Prove that  ∫e^x ∙((x^4 +2)/((1+x^2 )^(5/2) ))dx=((e^x {1+x^2 +x})/((1+x^2 )^(3/2) ))+C
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int\mathrm{e}^{\mathrm{x}} \centerdot\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} }\mathrm{dx}=\frac{\mathrm{e}^{\mathrm{x}} \left\{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right\}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }+\mathrm{C} \\ $$
Commented by Ar Brandon last updated on 03/Dec/20
Commented by Ar Brandon last updated on 03/Dec/20
I don't understand the third line
Commented by Ar Brandon last updated on 03/Dec/20
Alright ! I got it ✋

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