document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014579>Question 1014579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem: \r<BR>\n" );
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document.write( "3a. The antiderivative of f(x)=2/x is written as f(x)=2In|x|. Why must the absolute value symbol be used? \r<BR>\n" );
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document.write( "3b. By applying the rules for natural logarithms, how could the answer in question 3a. be expressed so that the absolute value symbol is not required? \r<BR>\n" );
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document.write( "Thank-you, your help is always appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630950 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=630950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> *********************************************<BR>\n" );
document.write( "3a) ln(x) is defined only for x > 0, hence |x| ensures x > 0<BR>\n" );
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document.write( "3b) Take the integral<BR>\n" );
document.write( "integral 2/x dx<BR>\n" );
document.write( "Factor out constants<BR>\n" );
document.write( "2 integral 1/x dx<BR>\n" );
document.write( "The integral of 1/x is log(x), therefore<BR>\n" );
document.write( "Antiderivative of 2/x = 2log(x)+constant where x > or equal to 1<BR>\n" );
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