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Evaluate int[f(x)g^(n)(x)-f^(n)(x)g(x)]...

Evaluate `int[f(x)g^(n)(x)-f^(n)(x)g(x)]dx`

Text Solution

Verified by Experts

The correct Answer is:
`f(x)g'(x)-f'(x)g(x)+C`
`int[f(x)g^(n)(x)-f^(n)(x)g(x)]dx`
`=intf(x)g^(n)(x)dx-int f^(n)(x)g(x)dx`
` =(f(x)g'(x)-int f'(x)g'(x)dx)-(g(x)f'(x)-int g'(x)f'(x)dx)`
`=f(x)g'(x)-f'(x)g(x)+C`
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