How do I evaluate the integral ∫ x * e^(2x) dx using integration by parts?

Using LIATE, choose u = x and dv = e^(2x) dx. Applying ∫ u dv = uv - ∫ v du yields (1/4) * e^(2x) * (2x - 1) + C.

Why is water (H2O) bent with a 104.5° angle instead of linear or 109.5°?

Oxygen has 4 electron domains (2 bonds and 2 lone pairs). Strong lone pair repulsion compresses the ideal 109.5° tetrahedral angle to 104.5°.

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