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Determine the antilogarithm (base \(e\)) of \[ \int_0^1 \dfrac{x^3-1}{\ln x} \mathrm{d}x \]

Suppose \( s_t = \displaystyle{\lim_{n \to \infty}} \sum_{r=1}^{n} \dfrac{2^r}{t^{2^r}+1}\). Determine \(\dfrac{s_7}{s_{17}}\).

\[\large \begin{pmatrix} 0.3 & b & c \\ l & m & n \\ o & p & q \end{pmatrix} \]

If the matrix above is orthogonal, find the sum ...

If \(1024(11-5ix) = 11x^{10} + 20ix^9 \) for \(i = \sqrt{-1} \), then which of the following is true regarding the magnitude of \(x\)?

Let \(S= \dfrac{\dbinom{30}{0}}{71} - \dfrac{\dbinom{30}{1}}{72} + \dfrac{\dbinom{30}{2}}{73}- \dots +\dfrac{\dbinom{30}{30}}{101} \).

What is the multiplicative inverse of the ...

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