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B. O. PEIRCE
HOLLIS PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN

HARVARD UNIVERSITY

REVISED EDITION

GINN & COMPANY

BOSTON , NEW YORK · CHICAGO · LONDON

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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

TABLE OF INTEGRALS.

I. FUNDAMENTAL FORMS.

1.

3.

log x.

xm +1

1. fade=az 2. S af() dx = a sf(a) dr.

Son 4. S 5. fedom 6. Sa+log adx = a*

S14792= tan-'x, or – etn-'x.

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wlien m is different from — 1.

m +1'

ex dx = ex.

7.

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11.

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=

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sin a da

COS X, or versin x.

ctn x dx = log sin x.

11. S 12. S si 13. Setn 14. St 16. Star 16. s seconda 17. Sesc

tan a da

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log cos x.

tan x sec x dx = secx.

= tan x.

cscx dx

ctn x.

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

9 dx + etc.

19 a.

u du = UV

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

- Swax Sudv= Svdu.

-Salon 20. r()dx = Sfa,dy.

19 b.

dv
U dx = UV
dx

dx.

da

II. RATIONAL ALGEBRAIC FUNCTIONS.

A. — EXPRESSIONS Involving (a + bx). The substitution of y or for x, where y = a + bx, z = (a + bx) / x, gives

1

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