Name: ) Evaluate the integral \( \int \frac{4 - 4x}{x(x^2 + 2)^2} dx \)
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First, we need to find the antiderivative of the integrand, which is: ∫(z^7 + 2)^4 dx We can use the substitution u = z^7 + 2, du/dz = 7z^6, dx = du/7z^6, to simplify the integral: ∫(z^7 + 2)^4 dx = (1/7) ∫u^4 du = (1/7) (u^5/5) + C Show more…
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