Use formal substitution to find the indefinite integral

Name: Use formal substitution to find the indefinite integral
Brand: Quizplus
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Question

Use formal substitution to find the indefinite integral  ​

Quizplus · Accepted Answer

Using formal substitution with u = x^4 + 1, du/dx = 4x^3, dx = du/4x^3, we get:

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

Thus, the answer is option D, 11ea8970_6a65_cbe1_861b_8f5caab2a939_TB1301_11.

Use Formal Substitution to Find the Indefinite Integral ​