Expression 30: "y" "e" Superscript, "H" left parenthesis, "x" , right parenthesis , Baseline equals Start integral from 0 to "x" , end integral, "e" Superscript, "H" left parenthesis, "t" , right parenthesis , Baseline times "g" left parenthesis, "t" , right parenthesis "d" "t" plus "C"yeHx=∫x0eHt·gtdt+C
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Expression 31: "y" equals StartFraction, Start integral from 0 to "x" , end integral, "e" Superscript, "H" left parenthesis, "t" , right parenthesis , Baseline times "g" left parenthesis, "t" , right parenthesis "d" "t" plus "C" Over "e" Superscript, "H" left parenthesis, "x" , right parenthesis , Baseline , EndFractiony=∫x0eHt·gtdt+CeHx
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Expression 32: "y" equals StartFraction, Start integral from 0 to "x" , end integral, "t" times "e" Superscript, "t" squared , Baseline "d" "t" plus "C" Over "e" Superscript, "x" squared , Baseline , EndFractiony=∫x0t·et2dt+Cex2
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Expression 33: "y" equals "e" Superscript, negative "x" squared , Baseline times left parenthesis, Start integral from 0 to "x" , end integral, "t" times "e" Superscript, "t" squared , Baseline "d" "t" plus "C" , right parenthesisy=e−x2·∫x0t·et2dt+C
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Den indre funktion
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Expression 35: "u" equals "x" squaredu=x2
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differentieres:
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Expression 37: StartFraction, "d" Over "d" "x" , EndFraction "u" equals 2 "x"ddxu=2x
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og dx isoleres:
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Expression 39: "d" "x" equals StartFraction, 1 Over 2 "x" , EndFraction "d" "u"dx=12xdu
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hvorefter u og dx indsættes:
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Expression 41: left bracket, "x" "e" Superscript, "u" , Baseline StartFraction, 1 Over 2 "x" , EndFraction , right bracket "d" "u"xeu12xdu
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Expression 42: left bracket, StartFraction, "e" Superscript, "u" , Baseline Over 2 , EndFraction , right bracket "d" "u" equals StartFraction, "e" Superscript, "x" squared , Baseline Over 2 , EndFraction plus "C"eu2du=ex22+C
Expression 44: "y" equals "e" Superscript, negative "x" squared , Baseline times left parenthesis, StartFraction, "e" Superscript, "x" squared , Baseline Over 2 , EndFraction plus "C" , right parenthesis Has graph. To audio trace, press ALT+T.y=e−x2·ex22+C
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Expression 45: "y" equals StartFraction, "e" Superscript, "x" squared minus "x" squared , Baseline Over 2 , EndFraction plus "C" "e" Superscript, negative "x" squared , Baseline Has graph. To audio trace, press ALT+T.y=ex2−x22+Ce−x2
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Expression 46: "y" equals 1 half plus "C" "e" Superscript, negative "x" squared , Baseline Has graph. To audio trace, press ALT+T.y=12+Ce−x2
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Expression 47: "C" equals 2.2 2C=2.22
negative 1.7−1.7
4.74.7
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Dummy d etc.
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"y" equals 1 half plus "C" "e" Superscript, negative "x" squared , Baseliney=12+Ce−x2
"e" Superscript, "H" left parenthesis, "x" , right parenthesis , BaselineeHx