document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=564912>Question 564912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> int 3x^(2) e^(-x) dx= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365744 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=365744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \int 3x^2e^{-x} dx\">\r<BR>\n" );
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document.write( "Begin by letting u = 3x^2 and dv = e^(-x) dx. Then du = 6xdx and v = -e^(-x). Applying integration by parts,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \int 3x^2e^{-x} dx = -3x^2e^{-x} - \int -6xe^{-x}dx = -3x^2e^{-x} + \int 6xe^{-x}dx\">\r<BR>\n" );
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document.write( "Again, we cannot really integrate 6xe^(-x) dx without using parts, so we let y = 6x, dz = e^(-x)dx --> dy = 6dx and z = -e^(-x). Hence,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -3x^2e^{-x} + \int 6xe^{-x}dx = -3x^2e^{-x} + (-6xe^{-x} - \int -6e^{-x} dx)\">\r<BR>\n" );
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document.write( "And just carry it out from there. Remember to add a constant when you are done, since antiderivatives are not uniquely determined and can differ by a constant. </SPAN>\n" );
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