(30) Z √ a 2 - x 2 dx = 1 2 x √ a 2 - x 2 + 1 2 a 2 tan -1 x √ a 2 - x 2 (31) Z x √ x 2 ± a 2 dx = 1 3 ( x 2 ± a 2 ) 3/2 (32) Z 1 √ x 2 ± a 2 dx = ln   x + √ x 2 ± a 2    (33) Z 1 √ a 2 - x 2 dx = sin -1 x a (34) Z x √ x 2 ± a 2 dx = √ x 2 ± a 2 (35) Z x √ a 2 - x 2 dx = - √ a 2 - x 2 (36) Z x 2 √ x 2 ± a 2 dx = 1 2 x √ x 2 ± a 2 ∓ 1 2 a 2 ln   x + √ x 2 ± a 2    (37) Z √ ax 2 + bx + c dx = b +2ax 4a √ ax 2 + bx + c+ 4ac - b 2 8a 3/2 ln   2ax + b +2 p a(ax 2 + bx + c)    Z x √ ax 2 + bx + c dx = 1 48a 5/2  2 √ a √ ax 2 + bx + c ( -3b 2 +2abx +8a(c + ax 2 ) ) +3(b 3 - 4abc) ln   b +2ax +2 √ a √ ax 2 + bx + c     (38) 4

(39) Z 1 √ ax 2 + bx + c dx = 1 √ a ln   2ax + b +2 p a(ax 2 + bx + c)    (40) Z x √ ax 2 + bx + c dx = 1 a √ ax 2 + bx + c- b 2a 3/2 ln   2ax + b +2 p a(ax 2 + bx + c)    (41) Z dx (a 2 + x 2 ) 3/2 = x a 2 √ a 2 + x 2 Integrals with Logarithms (42) Z ln ax dx = x ln ax - x (43) Z x ln x dx = 1 2 x 2 ln x - x 2 4 (44) Z x 2 ln x dx = 1 3 x 3 ln x - x 3 9 (45) Z x n ln x dx = x n+1  ln x n +1 - 1 (n + 1) 2  , n 6= -1 (46) Z ln ax x dx = 1 2 (ln ax) 2 (47) Z ln x x 2 dx = - 1 x - ln x x 5