Calculate $x^3 + \frac{1}{x^3}$

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How do you solve $\int_{0}^{\frac{\pi}{2}} \frac{2304\cos x}{(\cos 4x-8\cos 2x+15)^2} \,dx$

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Show that the solution of this (nonlinear) ODE cannot remain bounded as $t\to\infty$

Prove: $ T ◦ S $ is surjective iff $ $ T is surjective and $ ImS + KerT = V $

$ G/H \cong K $ and $ G/K \cong H\implies G \cong H \times K $

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Are all commutative, associative binary operations isomorphic to addition?

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