document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=210007>Question 210007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi all, I was hoping someone could show me how to find: <BR>\n" );
document.write( "the indefinite intergral of f (x) = 5x - 3x^2 + xsqrt(x) + 7 e^x<BR>\n" );
document.write( "and Hence calculate:  0&#8747;2 (5x-3x^2 + xsqrt(x) + 7e^x)dx<BR>\n" );
document.write( "(The zero should be beneath the 2, but I dont know how to fix the input)<BR>\n" );
document.write( "Any help would be great.<BR>\n" );
document.write( "-Nick.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159175 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is actually a definate integral if it has the bounds on it.  First off I would start by simplifying xsqrt(x).<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xsqrt%28x%29+=+x%2Ax%5E%281%2F2%29+=+x%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"xsqrt%28x%29+=+x%2Ax%5E%281%2F2%29+=+x%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <br>\r<BR>\n" );
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document.write( "so this becomes &#8747; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-3x%5E2+%2B+x%5E%283%2F2%29+%2B+7e%5Ex%29dx ALIGN=MIDDLE  ALT=\"%285x-3x%5E2+%2B+x%5E%283%2F2%29+%2B+7e%5Ex%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "*NOTE* I know this is a definite integral but I will leave the bounds off and then evaluate on the end, just because I can't get the bounds on the integral to come out either.  <br>\r<BR>\n" );
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document.write( "Now we just break it up piece by piece and this becomes<br>\r<BR>\n" );
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document.write( "5&#8747;x dx - 3&#8747;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > dx + &#8747; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%283%2F2%29%7D%7D+dx+%2B+7%26%238747%3Be%5Ex+dx%3Cbr%3E%0D%0A%0D%0Anow+we+evaluate+these+integrals.%3Cbr%3E%0D%0A%0D%0A5%281%2F2x%5E2%29+-+3%281%2F3x%5E3%29+%2B+2%2F5%28%7B%7B%7Bx%5E5%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >) + 7(e^x)<br>\r<BR>\n" );
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document.write( "Now we plug in the 2 and the 0 and in the first 3 terms the 0 doesn't matter<BR>\n" );
document.write( "5(1/2(2)^2) - 3(1/3(2)^3) + 2/5(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%5E5%2F2 ALIGN=MIDDLE  ALT=\"%282%29%5E5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 7(e^2-e^0)<BR>\n" );
document.write( "5(1/2(4)) - 3(1/3(8)) + 2/5(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832%29%5E1%2F2 ALIGN=MIDDLE  ALT=\"%2832%29%5E1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 7(e^2-1)<BR>\n" );
document.write( "5(2) - 8 + 2/5(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832%29%5E1%2F2 ALIGN=MIDDLE  ALT=\"%2832%29%5E1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 7e^2-7<BR>\n" );
document.write( "2 + 2/5(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832%29%5E1%2F2 ALIGN=MIDDLE  ALT=\"%2832%29%5E1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 7e^2-7<BR>\n" );
document.write( "-5 + 2/5(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832%29%5E1%2F2 ALIGN=MIDDLE  ALT=\"%2832%29%5E1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 7e^2<br>\r<BR>\n" );
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document.write( "I will leave you to plug that into your calculator and get the answer.  \r<BR>\n" );
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