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प्रश्न
Evaluate : `int e^x [(x + 3)/(x + 4)^2] dx`
उत्तर
Let I = `int e^x [(x + 3)/(x + 4)^2] dx`
= `int e^x [(x + 4 - 1)/(x + 4)^2] dx`
= `int e^x [(x + 4 )/(x + 4)^2 - 1/(x + 4)^2] dx`
= `int e^x [ 1/(x + 4) - 1/(x + 4)^2] dx`
= `(e^x)/(x + 4) + c`
`[therefore int e^x[f(x) + f'(x)] dx = e^x. f(x) + c]`
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