Barrons AP Calculus

(E) Use integration by  parts,  letting u   =   arctan  x   and dv  =   dx. Then

.

The Parts   Formula yields

.

(B) Hint:   Note    that

.

Or  multiply    the integrand   by   ,  recognizing that    the correct answer  is

equivalent  to  −ln |e−x    −   1|.

(D) Hint:   Expand  the numerator   and divide. Then    integrate   term    by  term.

(C) Hint:   Observe that    e2  ln u    =   u^2.

(A) Let u =     1    +  ln  y^2 =   1    +  2   ln  |y|;    integrate   .

(B) Hint:   Expand  and note    that

Use formulas    (9) and (7).

(E)