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Evaluate: ifintg(x)dx=g(x),t h e nintg(x...

Evaluate: `ifintg(x)dx=g(x),t h e nintg(x){f(x)+f^(prime)(x)}dx`

Text Solution

Verified by Experts

The correct Answer is:
`f(x)g(x)+C`
`int g(x){f(x)+f'(x)}dx`
`=int g(x)f(x)dx+int g(x)f'(x)dx `
`=f(x)(intg(x)dx)-int(f'(x)int g(x)dx)dx+int g(x)f'(x)dx`
`=f(x) g(x)-int g(x)f'(x)dx+int g(x)f'(x)dx+C`
`=f(x)g(x)+C " " [:' int g(x)dx=g(x)]`
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