You must have solved the integral of log of cosine

Calculus Level 5

I=0π/2x2log(sec(x))dxI=\displaystyle \int _{ 0 }^{ \pi /2 }{ { x }^{ 2 }\log ( \sec { (x) } ) dx }

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

Find ABCDE+1ABCDE+1

Details and Assumptions

1) A,B,C,D,EA,B,C,D,E are positive integers. Also ABCDEABCDE means product of the integers A,B,C,D,EA,B,C,D,E. Also base of log log is ee

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

3) ζ(s)=n=11ns\displaystyle \zeta{(s)} = \sum _{ n=1 }^{ \infty }{ \frac { 1 }{ { n }^{ s } } } .

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