Calculus, 2ADV C4 SM-Bank 3 If `f^{′}(x)= (x^2)/(x^3 + 1)` and `f(1)= log_e 2,` find `f(x)`. (3 marks) --- 6 WORK AREA LINES (style=lined) --- Show Answers Only `f(x) = 1/3 log_e(x^3 + 1) + 2/3 log_e 2` Show Worked Solution `f(x)` `=int f^{′}(x)\ dx` `=int (x^2)/(x^3 + 1)\ dx` `= 1/3 int (3x^2)/(x^3 + 1)\ dx` `=1/3 log_e |(x^3 + 1)|+c` `text(S)text(ince)\ \ f(1)= log_e 2,` `1/3 log_e 2+c` `= log_e 2` `c` `=2/3 log_e 2` `:.\ f(x) = 1/3 log_e(x^3 + 1) + 2/3 log_e 2`