document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=355862>Question 355862</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this equation:<BR>\n" );
document.write( "Evaluate the following integrals using trigonometric substitutions.<BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int+%28+x%5E2+%2F+%28+sqrt+%281-%28x%5E2%29+%29+%29%2C+dx+%29+ ALIGN=MIDDLE  ALT=\"+int+%28+x%5E2+%2F+%28+sqrt+%281-%28x%5E2%29+%29+%29%2C+dx+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int+%28+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%29%2C+dx+%29+ ALIGN=MIDDLE  ALT=\"+int+%28+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%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 #254082 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=254082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use a substitution.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sin%28u%29 ALIGN=MIDDLE  ALT=\"x=sin%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dx=cos%28u%29du ALIGN=MIDDLE  ALT=\"dx=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=x%5E2=%28sin%28u%29%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2=%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=1-x%5E2=1-%28sin%28u%29%29%5E2=%28cos%28u%29%29%5E2 ALIGN=MIDDLE  ALT=\"1-x%5E2=1-%28sin%28u%29%29%5E2=%28cos%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=sqrt%281-x%5E2%29=cos%28u%29 ALIGN=MIDDLE  ALT=\"sqrt%281-x%5E2%29=cos%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int+%28+x%5E2+%2F+%28+sqrt+%281-%28x%5E2%29+%29+%29%2C+dx+%29+=+int+%28+%28sin%28u%29%29%5E2+%2F+%28+cos%28u%29+%29+%2C+cos%28u%29du+%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+x%5E2+%2F+%28+sqrt+%281-%28x%5E2%29+%29+%29%2C+dx+%29+=+int+%28+%28sin%28u%29%29%5E2+%2C+du+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take it from there and solve for the integral in u, then back substitute to x.<BR>\n" );
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document.write( "Complete the square in the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int+%28+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%29%2C+dx+%29+=int+%28+1%2F+%28sqrt+%28x%5E2-4x%2B4%2B25%29%29+%29%2C+dx+%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+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%29%2C+dx+%29+=int+%28+1%2F+%28sqrt+%28%28x-2%29%5E2%2B25%29%29+%29%2C+dx+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x-2 ALIGN=MIDDLE  ALT=\"u=x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du=dx ALIGN=MIDDLE  ALT=\"du=dx\"   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+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%29%2C+dx+%29+=int+%28+1%2F+%28sqrt+%28u%5E2%2B25%29%29+%29%2C+du%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute again, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=5tan%28v%29 ALIGN=MIDDLE  ALT=\"u=5tan%28v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du=5%28sec%28v%29%5E2%29dv ALIGN=MIDDLE  ALT=\"du=5%28sec%28v%29%5E2%29dv\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2%2B25=25%28tan%28v%29%29%5E2%2B25=25%28%28tan%28v%29%29%5E2%2B1%29=25%28sec%28v%29%29%5E2 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=sqrt%28u%5E2%2B25%29=5%2Asec%28v%29 ALIGN=MIDDLE  ALT=\"sqrt%28u%5E2%2B25%29=5%2Asec%28v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%28u%5E2%2B25%29=1%2F%285%2Asec%28v%29%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%28u%5E2%2B25%29=1%2F%285%2Asec%28v%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+%28+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%29%2C+dx+%29+=int+%28+1%2F+%285%2Asec%28v%29%29%2C+5%28sec%28v%29%5E2%29dv%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+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%29%2C+dx+%29+=int+%28+sec%28v%29%2C+dv%29+ ALIGN=MIDDLE  ALT=\"+int+%28+1%2F+%28sqrt+%2829-4x%2B%28x%5E2%29%29+%29%2C+dx+%29+=int+%28+sec%28v%29%2C+dv%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take it from here and get the solution in v, back substitute for u, and then back substitute for x.<BR>\n" );
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document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );