If `inte^(xsec^(2)x-tanx)(x tanx -(sin2x)/2)dx=e^(f(x)).g(x)+c` then which of the following is/are incorrect?

Options

A. `f(0)` is equal to `=1`
B. number of solution (s) of the equation `(g(x))^(3//2)=1/(2sqrt(2))x^(3)` is 3
C. number of solution (3) of the equation `(g(x))^(3//2)=1/(2sqrt(2))^(3)` is 1
D. `f(x)` is an even function

Answer

A, B, D

Explanation

`inte^(xsec^(2)x-tanx)(xtanx-(sin2x)/2)dx=inte^(xsec^(2)x-tanx)((cos^(2)x)/2(xsec^(2)x-tanx)'+((cos^(2)x)/2))`
`=e^(xsec^(2)x-tanx).(cos^(2)x)/2+c`