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\[ \large\int_0^{\pi /2} \sqrt{1- \sin2x} \, dx \]

If the integral above can be written as \( a\sqrt b - c\), where \(a,b\) and \(c\) are positive integers with ...

Given that \[I=\displaystyle\int \limits^{\infty }_{0}\left( \dfrac{1-\cos ( \sqrt[3]{42} x) }{x^{2}} \right) ^{2}\, dx= A\pi.\] Find \(A\).

Bonus Find the closed ...

Let \( a_{n+1} = 2^{a_n} \) and \( b_{n+1} = 3^{b_n} \) both for \( n \ge 1.\)

If \( a_1 = 2 \) and \(b_1 = 3\), then find ...

Evaluate \[-\lim_{n\to\infty}\sum_{m=1}^{n}\prod_{k=1}^{m}\cos\left(\frac{2\pi{k}}{2m+1}\right) . \]

Find all infinitely differentiable functions \(f:\mathbb{R}\to\mathbb{R}\) that satisfy \[f(x)+f'(x)+f''(x)+\cdots =(f(x))^2\]

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