By formula (A) we have, making n = 3, and n = 2,

11

. (3.) — 5 log (x−1)+9 log (x—2) — — log (x−3)+C.

2

(8.) 22+x+log

(x-2)6(x+3)3

+C.

(2a-b) blog (x+b)+C.
(a-b)2

1 1

(10.)

(11).

· +2 + 2 log (x+2) — 2 log (2+1)+ 3 tan−x+C.

5 ̊x+2

25

25

25

(12.) ¦. log (x—1) — 2 log (x+1)+ log (x2+1)+C=loge √a^—1.

x+1

The first class of integrals which we shall consider are comprehended under the general form

x±TM (a2 ± x2)±3 dx

The integrals belonging to this class are, for the most part, obtained by the method of parts. Let us first take those of the form

* The limits and nature of the present work will not permit us to enter at any length upon a subject so extensive and intricate as the Integral Calculus. We shall therefore merely indicate the process by which some of the most useful integrals may be found, and refer the student who wishes to prosecute this subject to the masterly work of Lacroix.

c c c 2