Expression 28: "y" "e" Superscript, "A" left parenthesis, "x" , right parenthesis , Baseline equals Start integral from 0 to "x" , end integral, "b" left parenthesis, "t" , right parenthesis times "e" Superscript, "A" left parenthesis, "t" , right parenthesis , Baseline "d" "t" plus "C"yeAx=∫x0bt·eAtdt+C
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Expression 29: "y" equals StartFraction, Start integral from 0 to "x" , end integral, "b" left parenthesis, "t" , right parenthesis times "e" Superscript, "A" left parenthesis, "t" , right parenthesis , Baseline "d" "t" plus "C" Over "e" Superscript, "A" left parenthesis, "x" , right parenthesis , Baseline , EndFractiony=∫x0bt·eAtdt+CeAx
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Expression 30: "y" equals StartFraction, Start integral from 0 to "x" , end integral, sin left parenthesis, "t" , right parenthesis times "e" Superscript, ln left parenthesis, "t" , right parenthesis , Baseline "d" "t" plus "C" Over "e" Superscript, ln left parenthesis, "x" , right parenthesis , Baseline , EndFractiony=∫x0sint·elntdt+Celnx
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Expression 31: "y" equals StartFraction, Start integral from 0 to "x" , end integral, sin left parenthesis, "t" , right parenthesis times "t" "d" "t" plus "C" Over "x" , EndFractiony=∫x0sint·tdt+Cx
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Expression 32: "y" equals StartFraction, sin left parenthesis, "x" , right parenthesis minus "x" cos left parenthesis, "x" , right parenthesis plus "C" Over "x" , EndFractiony=sinx−xcosx+Cx
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Expression 33: "y" equals negative cosine "x" plus StartFraction, sin "x" plus "C" Over "x" , EndFractiony=−cosx+sinx+Cx
Expression 39: StartFraction, left parenthesis, Start integral from 0 to "x" , end integral, "b" left parenthesis, "t" , right parenthesis times "e" Superscript, "A" left parenthesis, "t" , right parenthesis , Baseline "d" "t" , right parenthesis plus "C" Over "x" , EndFraction∫x0bt·eAtdt+Cx
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Expression 40: "y" equals StartFraction, left parenthesis, "B" left parenthesis, "x" , right parenthesis times "e" Superscript, "A" left parenthesis, "x" , right parenthesis , Baseline minus Start integral from 0 to "x" , end integral, "B" left parenthesis, "t" , right parenthesis times left parenthesis, "a" left parenthesis, "t" , right parenthesis times "e" Superscript, "A" left parenthesis, "t" , right parenthesis , Baseline , right parenthesis "d" "t" , right parenthesis plus "C" Over "x" , EndFractiony=Bx·eAx−∫x0Bt·at·eAtdt+Cx
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Expression 41: "y" equals StartFraction, left parenthesis, negative cos left parenthesis, "x" , right parenthesis times "e" Superscript, ln left parenthesis, "x" , right parenthesis , Baseline minus Start integral from 0 to "x" , end integral, minus cos left parenthesis, "t" , right parenthesis times "a" left parenthesis, "t" , right parenthesis times "e" Superscript, ln left parenthesis, "t" , right parenthesis , Baseline "d" "t" , right parenthesis plus "C" Over "x" , EndFractiony=−cosx·elnx−∫x0−cost·at·elntdt+Cx
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Expression 42: "y" equals StartFraction, left parenthesis, negative cos left parenthesis, "x" , right parenthesis times "x" minus Start integral from 0 to "x" , end integral, minus cos left parenthesis, "t" , right parenthesis times StartNestedFraction, 1 NestedOver "t" , EndNestedFraction times "t" "d" "t" , right parenthesis plus "C" Over "x" , EndFractiony=−cosx·x−∫x0−cost·1t·tdt+Cx
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Expression 43: "y" equals StartFraction, left parenthesis, negative cos left parenthesis, "x" , right parenthesis times "x" minus left parenthesis, negative sin "x" , right parenthesis , right parenthesis plus "C" Over "x" , EndFractiony=−cosx·x−−sinx+Cx
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Expression 44: "y" equals StartFraction, sin left parenthesis, "x" , right parenthesis minus cos left parenthesis, "x" , right parenthesis times "x" plus "C" Over "x" , EndFractiony=sinx−cosx·x+Cx
44
går gennem et punkt ( 1 ; 2 ),
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der fastlægger konstanten C:
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Expression 47: 2 equals StartFraction, sin left parenthesis, 1 , right parenthesis minus 1cos left parenthesis, 1 , right parenthesis plus "C" Over 1 , EndFraction2=sin1−1cos1+C1
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Expression 48: "C" equals 2 minus sine left parenthesis, 1 , right parenthesis plus 1cosine left parenthesis, 1 , right parenthesisC=2−sin1+1cos1
equals=
1.6 9 8 8 3 1 3 2 1 0 61.69883132106
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Punktet ( 1 ; 2 )
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Animation
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Expression 52: "y" equals StartFraction, sin left parenthesis, "x" , right parenthesis minus "x" cos left parenthesis, "x" , right parenthesis plus "C" Subscript, 1 , Baseline Over "x" , EndFractiony=sinx−xcosx+C1x