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प्रश्न
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
उत्तर
`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`
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