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 ² 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 ³ 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 µ µ µ a x + p a ( ax + b ) µ µ µ 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 µ µ µ a x + p a ( ax + b ) µ µ µ + C (28) * c ± 2007. From http://integral-table.com, last revised December 6, 2007. This material is provided as is without warranty or representation
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integral-table - Table of Integrals Basic Forms xn dx = 1...

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