Barrons AP Calculus - David Bock
(C) Use formula (6) with ...
(A) Use formula (5) with u = 4t^2 ; du = 8t dt; ...
(A) Using the Half-Angle Formula (23) with α = 2x yields ...
(E) Use formula (6): ...
(B) Integrate by parts. Let u = x and dv = cos x dx. Then du = dx and v = sin x. The given integral equals ...
(D) Replace by sec^2 3 u; then use formula (9): ...
(C) Rewrite using u = 1 + sin x and du = cos x dx as Use formula (3). ...
(B) The integral is equivalent to Use formula (12). ...
(E) Use formula (13) with ...
(A) Replace sin 2x by 2 sin x cos x; then the integral is equivalent to where u = 1 + cos^2 x and du = −2 sin x cos x dx. Use ...
(D) Rewriting in terms of sines and cosines yields ...
(E) Use formula (7). ...
(C) Replace by csc^2 2 x and use formula (10): ...
(E) Let u = tan−1 y; then integrate The correct answer is ...
(A) Replacing sin 2θ by 2 sin θ cos θ yields ...
39. (C) ...
(B) Rewrite as and use formula (8). ...
(E) Use formula (4) with u = ex − 1; du = ex dx. ...
(D) Use partial fractions; find A and B such that Then x − 1 = A(x − 2) + Bx. Set x = 0: −1 = −2A and Set x = 2: 1 = 2B and So ...
(A) Use formula (15) with u = x^2 ; du = 2x dx; ...
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