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Find an anti-derivative of the functio...

Find an anti-derivative of the function `f(x)\ g''(x)-` `f''(x)\ g(x)`

Text Solution

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Given integration,
`I=f(x)g''(x)-f''(x) g(x) dx`
`=int fg''dx -int f'' g dx`
Let `I_2=int fg''dx`
`=f int g''dx-intf'*g' dx`
`=fg'-(f'intg'dx-intf''*gdx`
`=fg'-f'g+intf''gdx`
`therefore I=( fg'-f'g+intf''gdx)-intf''gdx`
`=fg'-f'g+c`
`=f(x)g'(x)-f'(x)g(x)+c`
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