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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 54 "Click on a box with a + inside to
 expland the section." }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Substitu
tions" }}{PARA 0 "" 0 "" {TEXT -1 79 "Maple can do substitutions for y
ou.  I'm not sure how valuable this is, though." }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 28 "R:=Int((sin^2)(x)*cos(x),x);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "R1:=changevar(u=sin(x),R,u);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "S:=Int((2+3*x)^3,x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "S1:=changevar(u=2+3*x,S,u);" }}}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "Integration by parts" }}{PARA 0 "
" 0 "" {TEXT -1 67 "Here are some examples of integrals which use inte
gration by parts." }}{PARA 0 "" 0 "" {TEXT -1 101 "Each problem is gro
uped into a section.  You can make sections like this by highlighting \+
the section," }}{PARA 0 "" 0 "" {TEXT -1 96 "then pressing the right a
rrow key above (just under the word Options).  Then you can add a titl
e" }}{PARA 0 "" 0 "" {TEXT -1 96 "to the section.  You can compress or
 expand each section by clicking on the box at the beginning" }}{PARA 
0 "" 0 "" {TEXT -1 74 "of the section.  You can begin a section by usi
ng Insert, Section (above)." }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Exa
mple 1" }}{PARA 0 "" 0 "" {TEXT -1 70 "The box to the left of \"Exampl
e 1\" can be clicked to shrink this part." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "a:=x*exp(x);" }{TEXT -1 30 "Define an expression call
ed a." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:=int(a,x);" }}}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Example 2" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "a:=x*cos(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "b:=int(a,x);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 
"Example 3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "a:=x*ln(x);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:=int(a,x);" }}}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 9 "Example 4" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "a:=(x^3)*sqrt(x^2+3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "b:=int(a,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 50 "c:=(1/3)*x^2*(x^2+3)^(3/2) -(2/15)*(x^2+3)^(5/2); " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "simplify(b-c); " }{TEXT -1 29 "Thes
e two are really the same" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Exa
mple 5" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:=ln(x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:=int(a,x);" }}}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 9 "Example 6" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "a:=(x^n)*ln(x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:=int(a,x);" }}}}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 17 "Partial Fractions" }}{PARA 0 "" 0 "" 
{TEXT -1 55 "Here are some examples which require partial fractions." 
}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Example 1" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "a:=(x^2+2*x)/((x+1)^2);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "b:=int(a,x);" }}}}{SECT 0 {PARA 3 "" 0 "" 
{TEXT -1 9 "Example 2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "a:=
1/(x^2+x-6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:=int(a,x)
;" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 23 "Trigonometric integrals" 
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 167 "Note that Maple can do the inte
grals, but its answer is not always in the simplest form, nor does it \+
always look like what we get using substitutions and other tricks." }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "int((sin^3)(x),x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "diff((1/3)*(cos^3)(x)-cos(x)
,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "int(cos(x)*(sin^2)(
x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int((cos^3)(x)*(s
in^4)(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "int((sin^4)
(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(tan(x),x);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "int(tan(x)*sec(x)^2,x);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(1/sqrt(1-x^2),x);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "int((x^2)/sqrt(4-x^2),x);" 
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