An Elementary Treatise On the Differential Calculus Founded On the Method of Rat
An Elementary Treatise On the Differential Calculus Founded On the Method of Rat
John Minot Rice
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[Ex. II. dx i x a sec a a tan a 47- f dx i x_ } x* 2ax sec a + a* ' 20 tan a * x 2ax sec a + a 2a tan a x a sec a + a tan a 4/2 2. * 2 3 4/2 lOg T-. 12 & 2X 2 + 34/2 / 55. {, 3_/!^ + l, 58. i i + x a ^a ^^^ 6 . * + * T ' lifc I^* W + 3 1, ^1 4/2 x - log 1- tan ' O . -/ X + 2 . 2 . X + I I . X 2 54. J 5 AY, log 1 lOg :' + I V . I 7- II. ] EXAMPLES. log x log (i 4- x) log ( i + x*) tan - l x. /( x* i i, x* x + i 60. -5 a dx, -log-^ . [*+*-! S \ i / J, x dx \ . X 2 ^$ x 62. , -log- - -\ -tan- 1 -^... . * * T^ *7 O/ V-l-'5 *7 /i/-? j x x -- 12 7 x -\- 2 7 r3 i . ^r i 4 log . T+7 64 . ^, a 20, a 40 x a xdx / f 4- ^T . " X I I 4^7)' ^ ^ N tanrI ^ + ^~ 32 ELEMENTARY METHODS OF INTEGRATION. [Ex. II. [__*_ ! * (. , 3 v, \ * 3 H 3 lOg 3 ' . x* (a + far) $ax* $a or / 74. Find the whole area enclosed by both loops of the curve ^J 75. Find the area enclosed between the asymptote corresponding to x = a, and the curve \y 76.
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