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Evaluate the following indefinite integrals. 2. x 1+x4 dx

Evaluate the following indefinite integrals. 2. x 1+x4 dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Evaluate the following indefinite integrals. X 2. S dx 1+x4
Transcribed Image Text:Evaluate the following indefinite integrals. X 2. S dx 1+x4
Expert Solution
Step 1: "Introduction to the solution"

We have  to evaluate  the  value  of  integral fraction numerator x d x over denominator open parentheses 1 plus x to the power of 4 close parentheses end fraction

Let I equals integral fraction numerator x d x over denominator open parentheses 1 plus x to the power of 4 close parentheses end fraction

Suppose open parentheses 1 plus x to the power of 4 close parentheses equals z

          rightwards double arrow 4 x cubed d x equals d z

          rightwards double arrow x d x equals fraction numerator 1 over denominator 4 x squared end fraction d z

Since, x to the power of 4 equals left parenthesis z minus 1 right parenthesis commaso x squared equals square root of z minus 1 end root


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