Chapter 5: Q. 38 (page 417)
Solve each of the integrals in Exercises 21–70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
Short Answer
The solution of the given integral is .
Chapter 5: Q. 38 (page 417)
Solve each of the integrals in Exercises 21–70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
The solution of the given integral is .
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Get started for freeSolve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
Explain why and are essentially the same integral after a change of variables.
Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
Explain why using trigonometric substitution with often involves a triangle with side lengths a and x and hypotenuse of length
Solve the integral: .
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