document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=565519>Question 565519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By a change of variables, determine the indefinite integral as follows:\r<BR>\n" );
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document.write( "integral (x^2 - 3x^4)^1/2 dx\r<BR>\n" );
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document.write( "The answer is supposed to be: (- (1 - 3x^2)^3/2) / 9\r<BR>\n" );
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document.write( "help me please </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365875 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=365875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By a change of variables, determine the indefinite integral as follows:\r<BR>\n" );
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document.write( "integral (x^2 - 3x^4)^1/2 dx<BR>\n" );
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document.write( "The integrand can be factored as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%281+-+3x%5E2%29%29+=+x%2Asqrt%281-3x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%281+-+3x%5E2%29%29+=+x%2Asqrt%281-3x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1+-+3x%5E2 ALIGN=MIDDLE  ALT=\"y+=+1+-+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy+=+-6x%2Adx ALIGN=MIDDLE  ALT=\"dy+=+-6x%2Adx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the integral can be written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F6%29%2Aint%28y%5E%281%2F2%29%2Cdy%29 ALIGN=MIDDLE  ALT=\"%28-1%2F6%29%2Aint%28y%5E%281%2F2%29%2Cdy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The antiderivative of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F6%29y%5E%281%2F2%29+=+%28-1%2F6%29%282%2F3%29%2Ay%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"%28-1%2F6%29y%5E%281%2F2%29+=+%28-1%2F6%29%282%2F3%29%2Ay%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Substituting back the expression for y gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281-3x%5E2%29%5E%283%2F2%29%2F9 ALIGN=MIDDLE  ALT=\"-%281-3x%5E2%29%5E%283%2F2%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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