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FormulaPage

# FormulaPage - You may nd the following expressions useful...

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You may find the following expressions useful. And you may not. But you may use them if they prove useful. “Known” Taylor series (all around x = 0): sin( x ) = x - x 3 3! + · · · + ( - 1) n x 2 n +1 (2 n + 1)! + · · · cos( x ) = 1 - x 2 2! + · · · + ( - 1) n x 2 n (2 n )! + · · · e x = 1 + x + x 2 2! + · · · + x n n ! + · · · (1 + x ) p = 1 + px + p ( p - 1) 2! x 2 + p ( p - 1)( p - 2) 3! x 3 + · · · “Known” integral expressions: Z x n ln x dx = 1 n + 1 x n +1 ln x - 1 ( n + 1) 2 x n +1 + C Z e ax sin( bx ) dx = 1 a 2 + b 2 e ax ( a sin( bx ) - b cos( bx )) + C Z e ax cos( bx ) dx = 1 a 2 + b 2 e ax ( a cos( bx ) + b sin( bx )) + C Z sin( ax ) sin( bx ) dx = 1 b 2 - a 2 ( a cos( ax ) sin( bx ) - b sin( ax ) cos( bx )) + C, a 6 = b Z cos(
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