Evaluate the integral .

Name: Evaluate the integral .
Brand: Quizplus
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Question

Evaluate the integral  . ​

Quizplus · Accepted Answer

This integral can be computed using the substitution method with u = x^2 - 2x + 1. Thus, du/dx = 2x - 2 and dx = du/(2x - 2). Substituting into the integral gives:

∫ (2x - 2) / (x^4 - 4x^3 + 8x^2 - 8x + 4) dx = ∫ du / u^2
= -1/u + C
= -1/(x^2 - 2x + 1) + C

Converting to a single fraction gives:

-1/(x^2 - 2x + 1) = -1/[(x-1)^2] = -1/(x^2 - 2x + 1) + 2/(x - 1)

Therefore, the answer is C, 11ea984b_b0f8_dd5f_9029_e7124b2f79d0_TB4005_11.

Evaluate the Integral . ​

Evaluate the Integral .