Barrons AP Calculus - David Bock
(B) Use formula (15) with u = sin θ; du = cos θ dθ. ...
(C) Use formula (6) with u = e2θ; du = 2e2θ dθ: ...
(B) Use formula (15) with ...
(C) Use the Parts Formula. Let u = x, dv = e−x dx; du = dx, v = −e−x. Then, ...
(C) See Example 44. ...
(D) The integral is of the form ...
(A) The integral has the form Use formula (18), with u = ex, du = ex dx. ...
(C) Let u = ln v; then Use formula (3) for ...
(E) Hint: ln ln x; the integral is ...
(B) Use parts, letting u = ln x and dv = x^3 dx. Then and The integral equals ...
(B) Use parts, letting u = ln and dv = dx. Then and v =. The integral equals 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 and The Parts Formula yields ...
(E) The integral has the form where ...
(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. ...
(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 t ...
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