# You must have solved the integral of log of cosine

Calculus Level 5

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

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

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