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Chapter 5: Q. 10 (page 417)
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
The differential du in terms of the differential dxis .
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For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
Solve the integral
Suppose you use polynomial long division to divide p(x) by q(x), and after doing your calculations you end up with the polynomial as the quotient above the top line, and the polynomial 3x − 1 at the bottom as the remainder. Then
Why don’t we need to have a square root involved in order to apply trigonometric substitution with the tangent? In other words, why can we use the substitution when we see , even though we can’t use the substitution unless the integrand involves the square root of? (Hint: Think about domains.)
Write as an algebraic function.
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