If C is arbitrary constant then dx is equal to

JEE MainMathematicsEasyIndefinite integration

If C is arbitrary constant
then $\int\left\lbrack f(x)g^{''}(x) - f^{''}(x)g(x) \right\rbrack$ dx is
equal to

Show answer and solution

\int\left( f(x)g^{''}(x) - f^{''}(x)g(x) \right)dx

= \int\ f(x)g^{''}(x)dx - \int{\ f}^{''}(x)g(x)dx

= f(x)g^{'}(x) - \int{\ f}^{'}(x)g^{'}(x) - \int{\ f}^{''}(x)g(x)

= f(x)g^{'}(x) - f^{'}(x)g(x) + \int{\ f}^{''}(x)g(x) - \int{\ f}^{''}(x)g(x)

= f(x)g^{'}(x) - f^{'}(x)g(x) + C

Source: Grass-G / M-12 Mathematics Paper 2 Nov.docx

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