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Is the formula given there correct?? Cuz by no way I am getting that formula and moreover in the example they've given, they treat -(1/x^2) as f(x) not (1/x).
So please tell me whether the formula is wrong or the example given is wrong or both are wrong.
Is the formula given there correct?? Cuz by no way I am getting that formula and moreover in the example they've given, they treat -(1/x^2) as f(x) not (1/x).
So please tell me whether the formula is wrong or the example given is wrong or both are wrong.
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The formula by itself is correct since [f e^x]' = [f + f'] e^x. However, in the example, the author mistook f' for f. The derivative of 1/x is -1/x^2, not the other way around.
Therefore the result of integral( (x-1)/x e^x dx ) is e^x/x.
Therefore the result of integral( (x-1)/x e^x dx ) is e^x/x.
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The formula is correct.
int e^x(f(x)+f'(x))
=> f(x) int e^x-int (f'(x) int e^x)+int e^x f'(x)
=> e^x f(x) [integrating by parts letting u as f(x) and v as e^x.]
int e^x(f(x)+f'(x))
=> f(x) int e^x-int (f'(x) int e^x)+int e^x f'(x)
=> e^x f(x) [integrating by parts letting u as f(x) and v as e^x.]
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The formula is correct, but they are using a different method of integration. I forget what it's called but it's definitely not integration by parts.
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the formula is correct