(E) Rewrite as and use formula (3).
(B) The integral is equal to sin 2θ dθ. Use formula (6) with u = 2θ; du
= 2 dθ.
(C) Use formula (6) with
(A) Use formula (5) with u = 4t^2 ; du = 8t dt; cos (4t^2 )(8t dt)
(A) Using the Half-Angle Formula (23) with α = 2 x yields
dx.
(E) Use formula (6): . (See Answer 23.)
(B) Integrate by parts. Let u = x and dv = cos x dx. Then du = dx and v =
sin x. The given integral equals x sin x − sin x dx.
(D) Replace by sec^2 3 u; then use formula (9):
(C) Rewrite using u = 1 + sin x and du = cos x dx as .
