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 New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: ELEMENTARY TRANSCENDENTAL FUNCTIONS 77 4.3.105 4.3.106 4.3.107 4.3.108 4.3.109 4.3.110 4.3.111 4.3.112 4.3.113 4.3.114 4.3.115 4.3.116 n Differentiation Formulas d - sin z=cos z dz d - cos z=-sin z dz d - tan z=sec2 z dz d - csc z=-csc z cot z dz d - sec z=sec z tan z dz d - cot z=-csc2 z dz Integration Formulas sin zdz=-cosz cos zdz=sinz tan zdz=-ln cosz=ln secz S S S z 1 1-cosz csc z dz=ln tan -=ln (csc z-coi z)=- In J 2 2 l+cos 2 4.3.117 Sseczdz=ln(secz+tanz)=lntan =Inverse Gudermannian Function ?r gd z=2 arctan ez-- 2 4.3.118 Scot zdz=ln sin z=-ln csc z 4.3.119 zn sinzdz=-z" cos z+n z"-l cos zdz S S 4.3.120 4.3.121 s s z d z = - z cot z+ln sin z 1.3.123 z" cos zdz=z" sin z-n z"-l sin zdz S S 4.3.124 4.3.125 4.3.126 s---&dz=z tan z+ln cos z 4.3.127 sinm+' z COS"-' z m+n sinm z cos" z dz= S + H J s i n m z COS"-~ z dz sinm-' z cos"+' z =- m+n (m+n) +-Ssinm+ (m- 1) 4.3.128 Jsinm z cos" z (n-1) sinm-1 z cosn-1 z z COS" z dz (m#-n) 1 - dz dz (n> 1) S m+n-2 + n-1 sin" z cosn-2 z -1 (m-1) sinm-' z COS"-' z - - dz m+n--2 + m-1 Ssinm-2 z cosn z cot"-' 2 4.3.130 cot" z dz=- ~ -scotn-2 z dz (n# 1) S n- 1 The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States.