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$F'\left( x \right) = f''\left( x \right)$

$F'\left( x \right) = f'\left( x \right)$             

$F'\left( x \right) = f\left( x \right)$

$f'\left( x \right) = F\left( x \right)$

$f'\left( x \right) = F\left( x \right)$

$\int {f\left( x \right)dx}  = F\left( x \right)+C$

$\int {F\left( x \right)dx}  = f\left( x \right) + C$

$f'\left( x \right) = F'\left( x \right)$

$\int {f'\left( x \right)dx}  = f\left( x \right) + C$    

$\int {f\left( x \right)dx}  = f'\left( x \right) + C$

$\int {f'\left( x \right)dx}  = f''\left( x \right) + C$

$\int {f\left( x \right)dx}  = f''\left( x \right) + C$

$y = 12{x^3}$

$y = \dfrac{{3{x^5}}}{5} - 1$

$y = \dfrac{{3{x^5} + 1}}{5}$

$y = \dfrac{3}{5}{x^5} - \dfrac{3}{5}$

$y = \sin x + 1$         

$y = \cos x$   

$y = \cot x$

$y =  - \cos x$

$\int {\sin xdx}  = \cos x + C$            

$\int {dx}  = x + C$

$\int {{e^x}dx}  = {e^x} + C$

$\int {\dfrac{1}{x}dx}  = \ln \left| x \right| + C$