(E) The integral equals ; it is equivalent to , where
u = 1 − ln t.
(A) Replace u by x in the given integral to avoid confusion in applying
the Parts Formula. To integrate , let the variable u in the Parts
Formula be x, and let dv be sec^2 x dx. Then du = dx and v = tan x, so
(D) The integral is equivalent to . Use formula (4) on
the first integral and (18) on the second.
(D) The integral is equivalent to .
Use formula (17) on the first integral. Rewrite the second integral as
, and use (3).
(E) Rewrite: .
(B) Hint: Divide, getting .
(D) Letting u = sin θ yields the integral . Use formula (18).
