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integral-table

integral-table - Table of Integrals Basic Forms xn dx = 1...

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Table of Integrals * Basic Forms Z x n dx = 1 n + 1 x n +1 + c (1) Z 1 x dx = ln x + c (2) Z udv = uv - Z vdu (3) Z 1 ax + b dx = 1 a ln | ax + b | + c (4) Integrals of Rational Functions Z 1 ( x + a ) 2 dx = - 1 x + a + c (5) Z ( x + a ) n dx = ( x + a ) n +1 n + 1 + c, n 6 = - 1 (6) Z x ( x + a ) n dx = ( x + a ) n +1 (( n + 1) x - a ) ( n + 1)( n + 2) + c (7) Z 1 1 + x 2 dx = tan - 1 x + c (8) Z 1 a 2 + x 2 dx = 1 a tan - 1 x a + c (9) Z x a 2 + x 2 dx = 1 2 ln | a 2 + x 2 | + c (10) Z x 2 a 2 + x 2 dx = x - a tan - 1 x a + c (11) Z x 3 a 2 + x 2 dx = 1 2 x 2 - 1 2 a 2 ln | a 2 + x 2 | + c (12) Z 1 ax 2 + bx + c dx = 2 4 ac - b 2 tan - 1 2 ax + b 4 ac - b 2 + C (13) Z 1 ( x + a )( x + b ) dx = 1 b - a ln a + x b + x , a 6 = b (14) Z x ( x + a ) 2 dx = a a + x + ln | a + x | + C (15) Z x ax 2 + bx + c dx = 1 2 a ln | ax 2 + bx + c | - b a 4 ac - b 2 tan - 1 2 ax + b 4 ac - b 2 + C (16) Integrals with Roots Z x - adx = 2 3 ( x - a ) 3 / 2 + C (17) Z 1 x ± a dx = 2 x ± a + C (18) Z 1 a - x dx = 2 a - x + C (19) Z x x - adx = 2 3 a ( x - a ) 3 / 2 + 2 5 ( x - a ) 5 / 2 + C (20) Z ax + bdx = 2 b 3 a + 2 x 3 ax + b + C (21) Z ( ax + b ) 3 / 2 dx = 2 5 a ( ax + b ) 5 / 2 + C (22) Z x x ± a dx = 2 3 ( x ± 2 a ) x ± a + C (23) Z r x a - x dx = - p x ( a - x ) - a tan - 1 p x ( a - x ) x - a + C (24) Z r x a + x dx = p x ( a + x ) - a ln x + x + a + C (25) Z x ax + bdx = 2 15 a 2 ( - 2 b 2 + abx + 3 a 2 x 2 ) ax + b + C (26) Z p x ( ax + b ) dx = 1 4 a 3 / 2 h (2 ax + b ) p ax ( ax + b ) - b 2 ln a x + p a ( ax + b ) i + C (27) Z p x 3 ( ax + b ) dx = b 12 a - b 2 8 a 2 x + x 3 p x 3 ( ax + b ) + b 3 8 a 5 / 2 ln a x + p a ( ax + b ) + C (28) * c 2007. From http://integral-table.com, last revised December 6, 2007. This material is provided as is without warranty or representation about the accuracy, correctness or suitability of this material for any purpose. Some restrictions on use and distribution may apply, including the terms of the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. See the web site for details. The formula numbers

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