document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939809>Question 939809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> it's actually about calculus but i couldn't find any parts about it..<BR>\n" );
document.write( "i was solving integration of tan^-1(x) by parts :<BR>\n" );
document.write( "consider &#8747;tan^-1(x)x1 dx.<BR>\n" );
document.write( "so let u=tan^-1(x) and du/dx=1/(1^2+x^2)<BR>\n" );
document.write( "       dv/dx=1, so v=x.<BR>\n" );
document.write( "&#8747;tan^-1(x)dx = xtan^-1(x)-&#8747;(1/(1+x^2))(x)dx<BR>\n" );
document.write( "              = xtan^-1(x)-&#8747;(x/(1+x^2)dx<BR>\n" );
document.write( "              = xtan^-1(x)-(1/2)&#8747;(2x/(1+x^2))dx<BR>\n" );
document.write( "              = xtan^-1(x)-(1/2)tan^-1(x^2)+c.<BR>\n" );
document.write( "but the answer is xtan^-1(x)-(1/2)ln(1+(x^2))+c.<BR>\n" );
document.write( "                       Why??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573011 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=573011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note the integration by parts formula: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \int u \, dv = uv - \int v \, du\">\r<BR>\n" );
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document.write( "In this case, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \int v \, du = \int \frac{x}{1+x^2} \, dx \"> since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large v = x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large du = \frac{1}{1+x^2} \, dx \"> (you forgot x in the numerator)\r<BR>\n" );
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document.write( "Integrating <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{x}{1+x^2} \, dx\"> using the substitution <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large w = 1+x^2\"> gives <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{1}{2} \ln (1+x^2) + C\">, as desired. </SPAN>\n" );
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