document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442217>Question 442217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with the following promblem, does anyone know about integrals?<BR>\n" );
document.write( "Find the integral. <BR>\n" );
document.write( "4(2x+5)^3 dx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305016 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \int 4(2x+5)^3\,dx\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Begin with the substitution u = 2x + 5. Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\frac{du}{dx} = 2\">, then this implies that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?du = 2dx\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?dx = \frac{du}{2}\">. We substitute to obtain an integral in terms of u:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \int 4u^3\, (\frac{du}{2}) = \frac{1}{2} \int 4u^3\, du\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is easily integrable, using the power rule:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2} \int 4u^3\, du = \frac{1}{2} 4(\frac{u^4}{4}) + C = \frac{u^4}{2} + C\"> where C is a constant. Since we want our expression in terms of x instead of in terms of u, we back substitute to get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \int 4(2x+5)^3\, dx = \frac{(2x+5)^4}{2} + C\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );