(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