document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027913>Question 1027913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%2F%281%2Bcos%5E2%28x%29%29%29%2C+dx%2C+0%2C+pi%29 ALIGN=MIDDLE  ALT=\"int%28%28x%2F%281%2Bcos%5E2%28x%29%29%29%2C+dx%2C+0%2C+pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and please give detailed solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643129 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=643129\">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%28%28x%2F%281%2Bcos%5E2%28x%29%29%29%2C+dx%2C+0%2C+pi%29+=+2int%28%28x%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "by using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bcos2x%29%2F2+=+cos%5E2%28x%29 ALIGN=MIDDLE  ALT=\"%281%2Bcos2x%29%2F2+=+cos%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Now let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi+-+y ALIGN=MIDDLE  ALT=\"x+=+pi+-+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute into the second integral.\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2int%28%28x%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29++=+2int%28%28%28pi-y%29%2F%283%2Bcos2y%29%29%2C+%28-dy%29%2C+pi%2C+0%29+=+2int%28%28%28pi-y%29%2F%283%2Bcos2y%29%29%2C+dy%2C+0%2C+pi%29+=+2int%28%28pi%2F%283%2Bcos2y%29%29%2C+dy%2C+0%2C+pi%29-2int%28%28y%2F%283%2Bcos2y%29%29%2C+dy%2C+0%2C+pi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Aint%28%281%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29-2int%28%28x%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4int%28%28x%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29+=+2%2Api%2Aint%28%281%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "==><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29+=+%28pi%2F2%29int%28%281%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%281%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29+=+%281%2F2%29int%28%281%2F%28sin%5E2%28x%29+%2B+2cos%5E2%28x%29%29%29%2C+dx%2C+0%2Cpi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , by letting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=++3sin%5E2%28x%29+%2B+3cos%5E2%28x%29 ALIGN=MIDDLE  ALT=\"3+=++3sin%5E2%28x%29+%2B+3cos%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos2x+=+cos%5E2%28x%29+-+sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cos2x+=+cos%5E2%28x%29+-+sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+%281%2F%28sin%5E2%28x%29%2B2cos%5E2%28x%29%29%29%2C+dx%2C0%2Cpi%29+=+int%28+%28csc%5E2%28x%29%2F%281%2B2cot%5E2%28x%29%29%29%2C+dx%2C0%2Cpi%29++=+%28-1%2Fsqrt%282%29%29int%28%281%2F%281%2B%28sqrt%282%29%2Acotx%29%5E2%29%29%2C+d%28sqrt%282%29%2Acotx%29%2C+0%2C+pi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2Fsqrt%282%29%29%28tan%5E-1%28sqrt%282%29%2Acotx%29%29%5B0%5D%5Epi+=+%28-1%2Fsqrt%282%29%29%28tan%5E-1%28-infinity%29+-+tan%5E-1%28infinity%29%29+=+%28-1%2Fsqrt%282%29%29%28-pi%2F2-pi%2F2%29+=+pi%2Fsqrt%282%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29+=+%28pi%2F4%29%2Aint%28+%281%2F%28sin%5E2%28x%29%2B2cos%5E2%28x%29%29%29%2C+dx%2C0%2Cpi%29+=+%28pi%2F4%29%2A%28pi%2Fsqrt%282%29%29+=+pi%5E2%2F%284sqrt%282%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28x%2F%281%2Bcos%5E2%28x%29%29%29%2C+dx%2C+0%2C+pi%29+=+2int%28%28x%2F%283%2Bcos2x%29%29%2C+dx%2C+0%2C+pi%29+=2pi%5E2%2F%284sqrt%282%29%29+=+pi%5E2%2F%282sqrt%282%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );