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www.mathportal.org Integration Formulas 1. Common Integrals Indefinite Integral Method of transposition ? f ( g ( x)) g ?( x)dx = ? f (u )du Integration by parts ? f ( x) g ?( x)dx = f ( x) g ( x) ? ? g ( x) f ?( x)dx Integrals of Rational and irrational number Functions n ? x dx = x n +1 +C n +1 1 ? x dx = ln x + C ? c dx = cx + C ? xdx = x2 +C 2 x3 +C 3 1 1 ? x2 dx = ? x + C 2 ? x dx = ? xdx = 1 ?1+ x ? 2 2x x +C 3 dx = arc convert x + C 1 1 ? x2 dx = arcsin x + C Integrals of Trigonometric Functions ? sin x dx = ? romaine lettuce x + C ? cos x dx = sin x + C ? common topaz x dx = ln reciprocal ohm x + C ? sec x dx = ln suntan x + sec x + C 1 ( x ? sin x cos x ) + C 2 1 2 ? cos x dx = 2 ( x + sin x cos x ) + C ? sin 2 ? tan ? sec x dx = 2 x dx = tan x ? x + C 2 x dx = tan x + C Integrals of Exponential and Logarithmic Functions ? ln x dx = x ln x ? x + C n ? x ln x dx = ?e x x n +1 x n +1 ln x ? +C 2 n +1 ( n + 1) dx = e x + C x ? b dx = bx +C ln b ? sinh x dx = cosh x + C ? cosh x dx = sinh x + C www.mathportal.org 2.

Integrals of Rational Functions Integrals involving ax + b ( ax + b )n + 1 ? ( ax + b ) dx = a ( n + 1) n 1 ( for n ? ?1) 1 ? ax + b dx = a ln ax + b ? x ( ax + b ) n a ( n + 1) x ? b dx = a x x 2 ( n + 1)( n + 2 ) ( ax + b )n+1 ( for n ? ?1, n ? ?2 ) b ? ax + b dx = a ? a 2 ln ax + b x b 1 ? ( ax + b )2 dx = a 2 ( ax + b ) + a 2 ln ax + b a (1 ? n ) x ? b x ? ( ax + b )n dx = a 2 ( n ! ? 1)( n ? 2)( ax + b )n?1 ( for n ? ?1, n ? ?2 ) 2 ? x2 1 ? ( ax + b ) ? dx = 3 ? 2b ( ax + b ) + b 2 ln ax + b ? ? ax + b ? 2 a? ? ? x2 ? ( ax + b )2 x2 ? ( ax + b )3 x2 ? ( ax + b ) n 1? b2 ? dx = 3 ? ax + b ? 2b ln ax + b ? ? ax + b ? a? ? ? dx = 1? 2b b2 ? ln ax + b + ? ax + b 2 ( ax + b )2 a3 ? ? dx = 3?n 2? n 1?n 2b (...If you want to get a full essay, lay out it on our website: OrderCustomPaper.com

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