The integral equals .(B) Use parts, letting u = ln η and dv = dx. Then and v = η. The
integral equals η ln .(B) Rewrite ln x^3 as 3 ln x, and use the method of Answer 54.(D) Use parts, letting u = ln y and dv = y −^2 dy. Then du = dy and v = − . The Parts Formula yields .
(E) The integral has the form , where u = ln v: (A) By long division, the integrand is equivalent to .(C) ; use formula (18) with u = x + 1.(D) Multiply to get .(C) See Example 45. Replace x by θ.