document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025369>Question 1025369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the integral the integral of the product of the quantity x times the square root of 1 minus x, dx.\r<BR>\n" );
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document.write( " negative x squared over 3 times the quantity 1 minus x raised to the three-halves power, plus C\r<BR>\n" );
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document.write( " x squared over 3 times the quantity 1 minus x raised to the three-halves power, plus C\r<BR>\n" );
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document.write( " the quotient of the quantity 2 minus 3 times x and 2 times the square root of the quantity 1 minus x, plus C\r<BR>\n" );
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document.write( " negative 2 divided by 15 times the quantities 2 plus 3 times x and the quantity 1 minus x raised to the three halves power, plus C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640713 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=640713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28x%2Asqrt%281-x%29%2Cdx%29 ALIGN=MIDDLE  ALT=\"int%28x%2Asqrt%281-x%29%2Cdx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Integrate by parts,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28v%2Cdu%29=uv-int%28u%2Cdv%29 ALIGN=MIDDLE  ALT=\"int%28v%2Cdu%29=uv-int%28u%2Cdv%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du=%281-x%29%5E%281%2F2%29dx ALIGN=MIDDLE  ALT=\"du=%281-x%29%5E%281%2F2%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x ALIGN=MIDDLE  ALT=\"v=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=int%28%281-x%29%5E%281%2F2%29%2Cdx%29=-%282%2F3%29%281-x%29%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"u=int%28%281-x%29%5E%281%2F2%29%2Cdx%29=-%282%2F3%29%281-x%29%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv=dx ALIGN=MIDDLE  ALT=\"dv=dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=uv=-%282%2F3%29x%281-x%29%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"uv=-%282%2F3%29x%281-x%29%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28u%2Cdv%29=-%282%2F3%29int%28%281-x%29%5E%283%2F2%29%2Cdx%29=-%282%2F3%29%28-%282%2F5%29%29%281-x%29%5E%285%2F2%29=%284%2F15%29%281-x%29%5E%285%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting it all together,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28x%2Asqrt%281-x%29%2Cdx%29=-%282%2F3%29x%281-x%29%5E%283%2F2%29-%284%2F15%29%281-x%29%5E%285%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28x%2Asqrt%281-x%29%2Cdx%29=%281-x%29%5E%283%2F2%29%28-%2810%2F15%29x-%284%2F15%29%281-x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-10x-4%281-x%29%29 ALIGN=MIDDLE  ALT=\"int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-10x-4%281-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-10x-4%2B4x%29 ALIGN=MIDDLE  ALT=\"int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-10x-4%2B4x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-6x-4%29 ALIGN=MIDDLE  ALT=\"int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-6x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28x%2Asqrt%281-x%29%2Cdx%29=-%282%2F15%29%281-x%29%5E%283%2F2%29%283x%2B2%29 ALIGN=MIDDLE  ALT=\"int%28x%2Asqrt%281-x%29%2Cdx%29=-%282%2F15%29%281-x%29%5E%283%2F2%29%283x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );