Chapter 5: Q.3TB (page 416)
Explain why \(\int \frac{2x}{x^2+1}dx\) and \(\int \frac{1}{x\ln x}dx\)are essentially the same integral after a change of variables.
Short Answer
The final integral is same.
Chapter 5: Q.3TB (page 416)
Explain why \(\int \frac{2x}{x^2+1}dx\) and \(\int \frac{1}{x\ln x}dx\)are essentially the same integral after a change of variables.
The final integral is same.
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Solve each of the integrals in Exercises 39โ74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Solve the following two ways:
(a) with the substitution
(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
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