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integration_formulas

# integration_formulas - www.mathportal.org Integration...

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www.mathportal.org Integration Formulas 1. Common Integrals Indefinite Integral Method of substitution ( ( )) ( ) ( ) 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 Functions 1 1 n n x x dx C n + = + + 1 ln dx x C x = + c dx cx C = + 2 2 x xdx C = + 3 2 3 x x dx C = + 2 1 1 dx C x x = - + 2 3 x x xdx C = + 2 1 arctan 1 dx x C x = + + 2 1 arcsin 1 dx x C x = + - Integrals of Trigonometric Functions sin cos x dx x C = - + cos sin x dx x C = + tan ln sec x dx x C = + sec ln tan sec x dx x x C = + + ( ) 2 1 sin sin cos 2 x dx x x x C = - + ( ) 2 1 cos sin cos 2 xdx x x x C = + + 2 tan tan x dx x x C = - + 2 sec tan x dx x C = + Integrals of Exponential and Logarithmic Functions ln ln x dx x x x C = - + ( ) 1 1 2 ln ln 1 1 n n n x x x xdx x C n n + + = - + + + x x e dx e C = + ln x x b b dx C b = + sinh cosh x dx x C = + cosh sinh x dx x C = +

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www.mathportal.org 2. Integrals of Rational Functions Integrals involving ax + b ( ) ( ) ( ) ( ) 1 1 1 n n ax b ax b dx a fo n n r + + + = + ≠ - 1 1 ln dx ax b ax b a = + + ( ) ( ) ( )( ) ( ) ( ) 1 2 1 1 2 , 1 2 n n a n x b x ax b dx ax b a n n for n n + ≠ - + - + = + + + ≠ - 2 ln x x b dx ax b ax b a a = - + + ( ) ( ) 2 2 2 1 ln x b dx ax b a ax b a ax b = + + + + ( ) ( ) ( )( )( ) ( ) 1 2 1 2 1 , 2 1 n n a n x b x dx ax b a n n for n ax b n - - - = + - + - - ≠ - ( ) ( ) 2 2 2 3 1 2 ln 2 ax b x dx b ax b b ax b ax b a + = - + + + + ( ) 2 2 2 3 1 2 ln x b dx ax b b ax b ax b a ax
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integration_formulas - www.mathportal.org Integration...

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