Question

${ \boxed{ \bold \red{If \: \int f(x) \: dx = F(x), \: then \: find \int {f}^{ - 1} (x) \: dx }}}$​

Answer 1

Answer in the Attachment

mark me as Brainliest if I am Correct

Answer 2

${ \bold \red{u=f {}^{ - 1} (x), \: x = f(u), \: dx = f'(u)du}}$

$\bold \red{{ = \displaystyle \bold{\int \: u \: f'(u)}} \: du}$

$\displaystyle { \bold \red{ = \int{uf'(u) \: du}}}$

$\bold \red{ = uf(u) - \displaystyle \bold{\int f(u) \: du}}$

$\bold \red{ = f {}^{ - 1} (x)x - F(u)}$

$\bold \red{= xf {}^{ - 1} (x) - F( {f}^{ - 1} (x)}$