Mastering Technical Mathematics, Third Edition, 3rd Edition

Appendix 4

Table of Indefinite Integrals

 

 

Letters a, b, r, and s denote general constants; c denotes the constant of integration; f, g, and h denote functions; w, x, y, and z denote variables. The letter e represents the exponential constant (approximately 2.71828).

FUNCTION	INDEFINITE INTEGRAL
f (x) = 0	∫ f (x) dx = c
f (x) = 1	∫ f (x) dx = 1 + c
f (x) = a	∫ f (x) dx = a + c
f (x) = x	∫ f (x) dx = (1/2)x2 + c
f (x) = ax	∫ f (x) dx = (1/2)ax2 + c
f (x) = ax2	∫ f (x) dx = (1/3)ax3 + c
f (x) = ax3	∫ f (x) dx = (1/4)ax4 + c
f (x) = ax4	∫ f (x) dx = (1/5)ax5 + c
f (x) = ax−1	∫ f (x) dx = a ln |x| + c
f (x) = ax−2	∫ f (x) dx = −ax−1 + c
f (x) = ax−3	∫ f (x) dx = −(1/2)ax−2 + c
f (x) = ax−4	∫ f (x) dx = (−1/3)ax−3 + c
f (