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We know the integration formula "a raise to power x". / x | x a | a dx = ------ + C for base 10 logarithm ..........(i) | log a / Similarly for "e raise to power x". / x | x e | e dx = ------ + C for base e logarithm ......... (ii) | ln e /

We should memorize the formulas (i) & (ii) because it clear the basic concept and logical result are same and easy to remember.

Here ln e = 1 (because e^0 = 1 and by use logarithm property we get ln e = 1 )

When simplify the (ii) we get x x e e x = ------ = ------ = e ln e 1 / x x | e dx = e + C ......... (iii) / Integration formulas (ii) & (iii) are same formula and we mostly use (iii).

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(e = 2.7182818284 5904523536 0287471352 6624977572 4709369995 9574966967 6277240766 3035354759 4571382178 5251664274 ...)

1/n e = lim (1 + n) n->0 1 n e = lim (1 + ---) n->∞ n ∞ 1 e = ∑ --- n=0 k!

(x^0.1/0.1, x^0.2/0.2, x^1.1/1.1, x^2.2/2.2)

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