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Evaluate: ∫(x+3)e^x/(x+5)^3dx - Mathematics

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Evaluate:

`int((x+3)e^x)/((x+5)^3)dx`

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Solution

`int((x+3)e^x)/((x+5)^3)dx`

`=int((x+5-2)e^x)/((x+5)^3)dx`

`=int((x+5)/(x+5)^3-2/(x+5)^3)e^xdx`

`=int[1/(x+5)^2-2/(x+5)^3]e^xdx`

This is of the form

`int e^x[f(x)+f'(x)]dx=e^xf(x)+C`

`=>int[1/(x+5)^2-2/(x+5)^3]e^xdx`

`=e^x/(x+5)^2+C`

Concept: Integrals of Some Particular Functions
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