# Re: antiderivitives

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Posted by T.Gracken on November 01, 2002 at 12:42:23:

In Reply to: antiderivitives posted by chris on November 01, 2002 at 12:09:38:

: i think i have this problem done, but i don't know. the probelm is to find the antiderivitive of 1/x + 2/sq rt of x

: i got 2x^1.5/1.5 but i'm told its wrong

original problem: 1/x + 2/sqrt(x) [sqrt(something) is standard way of writing the "squareroot of something" in text]

I suggest rewrite: x-1 + 2x-1/2

*new antiderivative: antiderivative of x-1 is ln|x| {that is, natural log of absolute value of x. this is the case when exponent is -1}

so, to determine the antiderivative of two (or more) things added, find antiderivative of each thing and add the results.

here, antiderivative of x-1 + 2x-1/2

= ln|x| + (2x1/2)/(1/2)

use algebra to get

= ln|x| + 4x1/2, which is the same as

= ln|x| + 4*sqrt(x)

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