A:

SHORT TABLE OF INTEGRALS

BY

B. O. PEIRCE

HOLLIS PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN

HARVARD UNIVERSITY

REVISED EDITION

GINN & COMPANY

BOSTON NEW YORK CHICAGO LONDON

Since I cannot hope that these formulas are wholly free
from misprints, I shall be grateful to any person who will
call my attention to such errors as he may discover.

B. O. PEIRCE,

Harvard University, Cambridge.

COPYRIGHT, 1899

BY GINN & COMPANY

ALL RIGHTS RESERVED

35.6

The Athenæum Press

GINN & COMPANY. CAM-
BRIDGE MASSACHUSETTS

In the following formulas, u, v, w, and y represent any functions of x:

w dx + etc.

18. S(u+v+w+ etc.) dx = Sudx + S v dx + Sw

II. RATIONAL ALGEBRAIC FUNCTIONS.

A. - EXPRESSIONS INVOLVING (a + bx).

The substitution of ≈ = (a + bx)/x, gives

1

y or

2 for x, where y = a + bx,

21. S (a + bx)"dx = { SyTMdy.

1

23. Sx” (u+bx)TM dx = +1 SyTM (y — a)"dy.

Zn+1

x" (a + bx)m

Whence

1