(10) Z x a 2 + x 2 dx = 1 2 ln |a 2 + x 2 | (11) Z x 2 a 2 + x 2 dx = x - a tan -1 x a (12) Z x 3 a 2 + x 2 dx = 1 2 x 2 - 1 2 a 2 ln |a 2 + x 2 | (13) Z 1 ax 2 + bx + c dx = 2 4ac - b 2 tan -1 2ax + b 4ac - b 2 (14) Z 1 (x + a)(x + b) dx = 1 b - a ln a + x b + x ,a 6= b (15) Z x (x + a) 2 dx = a a + x + ln |a + x| (16) Z x ax 2 + bx + c dx = 1 2a ln |ax 2 +bx +c|- b a 4ac - b 2 tan -1 2ax + b 4ac - b 2 Integrals with Roots (17) Z x - a dx = 2 3 (x - a) 3/2 (18) Z 1 x ± a dx =2 x ± a (19) Z 1 a - x dx = -2 a - x 2
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