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

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Antiderivative formulas 1 1 when 1 1 ln | | p p kx kx x xd x p p x x e ed x k + =≠ + = = Example 35 2 Find an antiderivative 1 x xe d x x ++ Solution 32 5 4 1 15 4( 1 ) 1 5 x x pk x x x x xx e d x e + + = + + = With Constants 5 41 5 Find an antiderivative 1 ) 5 67 4 4 x x e d x e Substitution 1 () ' 1 Let ( 1 '( ) ln | ( ) | ) '( ) p p fx fx f xd x p p dx f uf x x ef x d x ux e dfd x + = + = = = Problem 2 3 Find an antiderivative 23 x dx x +
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Solution 3 2 3 32 1/2 3 2 Check (1/ 3)( 23 Let 1/2)(2 6 63 3)6 3 x dx x ux d du u x u xx + = == + += + Problem 2 Find an antiderivative 3 x dx Solution 2 2 2 12 3 3 1 Check 2 3 3 ln | | ln | 3 | x dx ux xd u x ud u u x x x =− = F(x)=ln(3x-x 2 ) f(x)=(2x-3)/(x 2 –3x) -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 0 0.5 1 1.5 2 2.5 3 Problem 3 2( 3 ) Find an antiderivative (1 ) xe d x Solution 3 3 3 3 ) (3 2 ) ) ) 3 3 (1 / 3) (1 / 3 Check ) 3 3) uu x x xed x ex xd du ee e =
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Example 6, p. 398 Find an antiderivative 1 xx d x Solution 1/2 3/2 5/2 3/ 1 25 / /2 2 (1 ) ) ) (3/ 2) (5 / 2) 3/ 2 (5 Check ) ) ) [1 ) 2 ] /) d x ux xu d u d x u u
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2.8 Class Notes - Antiderivative formulas x p +1 x dx = p +...

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