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Home » Evaluate the integral \(\int_0^1 (3x^2 + 2x) \, dx\). - Richter Guitar

Evaluate the integral \(\int_0^1 (3x^2 + 2x) \, dx\). - Richter Guitar

📅 May 3, 2026 👤 scraface

May 03, 2026

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Let $k^2 = \frac{144y^2 + 3600}{25}$. Then:
144y^2 + 3600 \equiv 0 \pmod{25} \Rightarrow 144y^2 \equiv -3600 \pmod...
Since $144 \equiv 19 \pmod{25}$ and $-3600 \equiv 0 \pmod{25}$, we get...
19y^2 \equiv 0 \pmod{25} \Rightarrow y^2 \equiv 0 \pmod{25} \Rightarro...
So let $y = 5k$. Substitute:
25x^2 = 144(25k^2) + 3600 = 3600k^2 + 3600 = 3600(k^2 + 1).
Divide both sides by 25:
x^2 = 144(k^2 + 1).
So $x^2 = 144(k^2 + 1) = (12)^2(k^2 + 1)$, hence $x = 12\sqrt{k^2 + 1}...
m^2 - k^2 = 1 \Rightarrow (m - k)(m + k) = 1.

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