Fluents. arc tang da xdx f xdx M. xTM(f+gx°)−1(a+bx2)3⁄4dx=x”y—1z3d.x arc tang ag-bfx 3 = / - / (f+gx)√(a+bx2) f+gx2 8 •x√(a+bx2)dx 340. ƒ+gx2 341. dx 331. f2 (f+gx)√(a+bx2) x*(f+gx)(√a+bx2) xy√z dr dx g dx = x2(ƒ+gx)√(a+bx2) x2+z ƒ2 dx g2 + $S-$ Sz + Putting ag2-bfg+cf2=k dx xdx 2ag-bf+(bg-2cf)x+2↓k√% y arc tang- 2-ky dx f x2dx 1 xdx f = = = = - S f+gx)√(a+bx+cx2) ge + f+gx)√(a+bx+cx2) dx f3 O. (aa—x1)±3dx. S dx Particular values, from x=0 to x = a. dx 1 = √(a*—x4) 2a (f+gx2)√(a+bx2) ̄ √(ag2—bfg) gz-(ag2-bfg) 2 + g2 dr VOL. IV. PART I. PP 1 1.3 1 1 3 + 2 4 4.6 2.4 1.3. 5 6 4.6.8 357. 358. M B. cosodo 2 359. Scos3pdp = (}} 360. M x 1 3.14159 M+N 361. M+1 Cosec 180° M+N 362. 3 3 = 12 sin 30+ sin 5 24 sin+16 5 3 15 15 6 1 5 80 30. 48 8 5 5 24 16 364. Ssino cosqdq=sin*+1¢ We have for the powers of sin ?, sin*4= 5 +16 1 N=4P+2; and sin*Q=±2N=1 sin N Fluents. hl 2 sin+4+1 ) cosp +2 hl cos 5 5 2. hl tang (45°+2) M d. sin cos-dø. = 3 cos33 3 cosp = (sin = ( sin20 4 1 = tang34 1 3 cos30 sin3p-sin tang3p-tang +7° = = 1 5 (- sin' + 10 sine sine)) 3 - seco 431. sin cos sin2+2) cosq 1 = 2 =cos+seco 3 1 3 2 sin5pdo 1 4 8 417. = sin40 sin2+ cos2p 3 3 3 cos Psin odo. φαφ. 1 cos5 4 cos⭑Q sin2@do cos3 = (sin34 + 1 sin 8 tang (45 (45° + 2) sin1 4 cost sin1odo sim cos p sinodo cos Q cos = 1 4 sinRødø Cos = 3 8 sin3p-sino)+ ht tang (45°+2) = tang p hl |