2.8 Class Notes - Antiderivative formulas x p 1 x dx = p 1...

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Antiderivative formulas 1 1 when 1 1 ln | | p p kx kx x x dx p p x dx x e e dx k + = + = = Example 3 5 2 Find an antiderivative 1 x x e dx x + + Solution 3 2 5 4 1 1 5 4 ( 1) 1 5 x x p kx p kx x e x dx e dx p k x x e dx x x e + + + + = + + = With Constants 3 2 5 4 1 5 Find an antiderivative 4 ( 1) 5 6 7 4 6 7 4 x x x x e dx x x e + + + + Substitution 1 ( ) ( ) ( ) ( ) '( ) 1 Let ( 1 '( ) ln | ( ) | ( ) '( ) ) '( ) p p f x f x f x f x f x dx p p f x dx f u f x x f x e f x dx u x e d f dx + = ≠ − = + = = = Problem 2 3 Find an antiderivative 2 3 x dx x +
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