MISCELLANEOUS ALGEBRAIC EXPRESSIONS. 33 where m<n, may be expressed as the sum of a number of partial fractions of the form A (x − a) √ a + bx + cx2 , and these can be integrated by the aid of equations given above. Thus, 34 MISCELLANEOUS ALGEBRAIC EXPRESSIONS. 232. Sƒ (x, Ŵc+Wa+bæ) dx where y' (a' + b'x) = a + bx and s is the least common multi ple of n, q, etc. 234. Sƒ(x, √a+bx+ x2) dæ ́2 √ a · z − b ̧ z2 √ a − bz +√a) (22 √a − bz +√a) dz =2Ss(2 1 22 - 1 22 (b − 2 u)2 V. TRANSCENDENTAL FUNCTIONS. sin x · ƒ (cos x) dx = — 236. Ssi -Sf f(cos x)d cos x. =Sf Ssin 237. Sc cos x · ƒ (sin x) dx = ƒ ƒ (sin æ) d sin æ. 238. . sin æ⋅f (sin x, cos x) dx = − where = cos x. Sƒ(√1 — 22, ñ)dz, 239. Sco where z = sin x. 240. Sƒ (sin x, cos x) π π 242. Sƒ (tan x) dx = — -Setn (1-x)d (1-x) fctn 2 sin x f(sin x) dx V1-2 sin2x where sin2x. 245. S 'cos x ⋅f (cos2x) dx √1 - k2 sin2x |