document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193638>Question 1193638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the integral of (x^2)(√5-x^2)dx using trigonometric substitution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825670 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int\,x^2\(\sqrt{5\,-\,x^2}\)\,dx\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{5\,-\,x^2}\"> looks like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{a\,-\,bx^2}\">, so substitute <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ \frac{a}{b}\sin(u)\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ =\ \sqrt{5}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{du}\(\sqrt{5}\sin(u)\)\ =\ \sqrt{5}\frac{d}{du}\sin(u)\ =\ \sqrt{5}\cos(u)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int\,x^2\(\sqrt{5\,-\,x^2}\)\,dx\ =\ \int\,\(\sqrt{5}\sin(u)\)^2\sqrt{5\,-\,\(\[\sqrt{5}\sin(u)\]^2\)}\,\(\sqrt{5}\cos(u)\)\,du\">\r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int\,\(5\sin^2(u)\)\,\sqrt{5\,-\,5\sin^2(u)}\,\sqrt{5}\cos(u)\,du\">\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{1\,-\,\sin^2(\varphi)}\ =\ \cos(\varphi)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int\,\(5\sin^2(u)\)\,\sqrt{5}\cos(u)\,\sqrt{5}\cos(u)\,du\ =\ \int\,25\sin^2(u)\cos^2(u)\,du\">\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin^2\varphi\cos^2\varphi\ =\ \frac{1\,-\,cos(4\varphi)}{8}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{25}{8}\,\int\,\(1\ -\ \cos(4u)\)\,du\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{25}{8}\,\[\int\,du\ -\ \int\,\cos(4u)\,du\]\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{25}{8}\,\[u\ -\ \frac{1}{4}\,\sin(4u)\]\ +\ C\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large u\ =\ \arcsin\(\frac{1}{\sqrt{5}}x\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{25}{8}\,\[\arcsin\(\frac{ 1 }{\sqrt{5}}x\)\ -\ \frac{1}{4}\,\sin\(4\arcsin\(\frac{1}{\sqrt{5}}x\)\)\]\ +\ C\">\r<BR>\n" );
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document.write( "Or if you prefer\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{25}{8}\,\[\sin^{-1}\(\frac{ 1 }{\sqrt{5}}x\)\ -\ \frac{1}{4}\,\sin\(4\sin^{-1}\(\frac{1}{\sqrt{5}}x\)\)\]\ +\ C\">\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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