document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356868>Question 356868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: <BR>\n" );
document.write( "Evaluate the integral <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int+%28+sin%5E2%283x%29cos%5E5%283x%29%2C+dx+%29+ ALIGN=MIDDLE  ALT=\"+int+%28+sin%5E2%283x%29cos%5E5%283x%29%2C+dx+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254798 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=254798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=3x ALIGN=MIDDLE  ALT=\"u=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du=3dx ALIGN=MIDDLE  ALT=\"du=3dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int+%28+sin%5E2%283x%29%2Acos%5E5%283x%29%2C+dx+%29=3%2Aint+%28+sin%5E2%28u%29%2Acos%5E5%28u%29%2C+du+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28u%29%29%5E2%2B%28cos%28u%29%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28sin%28u%29%29%5E2%2B%28cos%28u%29%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28u%29%29%5E2=1-%28sin%28u%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28cos%28u%29%29%5E2=1-%28sin%28u%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28u%29%29%5E4=1-%28sin%28u%29%29%5E4 ALIGN=MIDDLE  ALT=\"%28cos%28u%29%29%5E4=1-%28sin%28u%29%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int+%28+sin%5E2%283x%29%2Acos%5E5%283x%29%2C+dx+%29=3%2Aint+%28+sin%5E2%28u%29%2Acos%5E4%28u%29%2Acos%28u%29%2C+du+%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+%28+sin%5E2%283x%29%2Acos%5E5%283x%29%2C+dx+%29=3%2Aint+%28+sin%5E2%28u%29%2A%281-%28sin%28u%29%29%5E4%29%2Acos%28u%29%2C+du+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=sin%28u%29 ALIGN=MIDDLE  ALT=\"v=sin%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv=cos%28u%29du ALIGN=MIDDLE  ALT=\"dv=cos%28u%29du\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int+%28+sin%5E2%283x%29%2Acos%5E5%283x%29%2C+dx+%29=3%2Aint+%28+v%5E2%2A%281-v%5E2%29%5E2%2C+dv%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+%28+sin%5E2%283x%29%2Acos%5E5%283x%29%2C+dx+%29=3%2Aint+%28+v%5E2%2A%281-2v%5E2%2Bv%5E4%29%2C+dv%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+%28+sin%5E2%283x%29%2Acos%5E5%283x%29%2C+dx+%29=3%2Aint+%28+%28v%5E2-2v%5E4%2Bv%5E6%29%2C+dv%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "Now the problem is reduced to a simple polynomial integration.<BR>\n" );
document.write( "Integrate and then substitute back for v and then finally u.<BR>\n" );
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document.write( ".<BR>\n" );
document.write( "Additionally, this is not an algebra problem.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );