document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999361>Question 999361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Very confused on taking antiderivatives. In my class I am not allowed to use integrals, just math logical to solve this problem: e^(x/5) + sin(3x). I know it's sort of like figuring out what the function must have been before the derivative was taken but this keeps giving me trouble. I have to reverse the derivative and get it back to its original state. sin(3x) is simple enough for it to be +sin(3x) it must be a negative cosine and something for which cancels the 3 out so 1/3 therefore, -1/3cos(3x) would be the original. But the original of e^(x/5) this one baffles me. It's really the (x/5) that I don't get. How does undoing that work exactly? what must I do/understand first before getting its antiderivative/\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617035 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f'(x) = e^(x/5)dx<BR>\n" );
document.write( "Find f(x)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Let x/5 = u<BR>\n" );
document.write( "Then du = (1/5)dx<BR>\n" );
document.write( "dx = 5du<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "dy = e^u(5du)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "dy = 5e^u du<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Integrate to get:<BR>\n" );
document.write( "y = 5e^u<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute to get:<BR>\n" );
document.write( "y = 5e^(x/5)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "----------- </SPAN>\n" );
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