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Home » Evaluate the integral \( \int (3x^2 - 4x + 1) \, dx \). - Portal da AcÃºstica

Evaluate the integral \( \int (3x^2 - 4x + 1) \, dx \). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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First, expand both squared terms:
Add the two expressions:
f(x) = \sec^2 x + \cos^2 x + 2 + \csc^2 x + \sin^2 x - 2
f(x) = \sec^2 x + \csc^2 x + (\cos^2 x + \sin^2 x) + 2 - 2 = \sec^2 x...
Now express in terms of sine and cosine:
f(x) = \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} + 1 = \frac{\sin^2 x +...
Using the identity $ \sin(2x) = 2\sin x \cos x $, we have:
\sin x \cos x = \frac{1}{2} \sin 2x \Rightarrow \sin^2 x \cos^2 x = \f...
f(x) = \frac{1}{\frac{1}{4} \sin^2 2x} + 1 = \frac{4}{\sin^2 2x} + 1
Since $ 0 < x < \frac{\pi}{2} $, then $ 0 < 2x < \pi $, and $ \sin 2x...

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