You must have solved the integral of log of cosine

$I=\displaystyle \int _{ 0 }^{ \pi /2 }{ { x }^{ 2 }\log ( \sec { (x) } ) dx }$

If the value of $I$ can be represented as = $\dfrac{\pi}{A} \zeta{(B)} + \dfrac{{\pi}^{C} \log{D} }{E}$

Find $ABCDE+1$

Details and Assumptions

1) $A,B,C,D,E$ are positive integers. Also $ABCDE$ means product of the integers $A,B,C,D,E$ . Also base of $log$ is $e$

2)Remember $D$ is not divisible by a perfect power(power >1 ) of any integer.

3) $\displaystyle \zeta{(s)} = \sum _{ n=1 }^{ \infty }{ \frac { 1 }{ { n }^{ s } } }$ .