An Elementary Treatise On the Differential Calculus Founded On the Method of Rat

Cover 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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