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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving powers of the direct function and a power function > Involving powers of sin and power > Involving zalpha-1 sinnu(a z+b)





http://functions.wolfram.com/01.06.21.1047.01









  


  








Input Form





Integrate[z Sin[a z + b]^5, z] == (1/(3600 a^2)) (-5 (3 a z (150 Cos[b + a z] - 25 Cos[3 (b + a z)] + 3 Cos[5 (b + a z)]) + 25 (-18 Sin[b + a z] + Sin[3 (b + a z)])) + 9 Sin[5 (b + a z)])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List["z", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a", " ", "z"]], "+", "b"]], "]"]], "5"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["3600", " ", SuperscriptBox["a", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "5"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "a", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["150", " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "-", RowBox[List["25", " ", RowBox[List["Cos", "[", RowBox[List["3", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["3", " ", RowBox[List["Cos", "[", RowBox[List["5", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]]]], "+", RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "18"]], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["3", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["9", " ", RowBox[List["Sin", "[", RowBox[List["5", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]]]]]]]]








MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 150 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 25 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 25 </mn> <mo> &#8290; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["z_", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a_", " ", "z_"]], "+", "b_"]], "]"]], "5"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "5"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "a", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["150", " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "-", RowBox[List["25", " ", RowBox[List["Cos", "[", RowBox[List["3", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["3", " ", RowBox[List["Cos", "[", RowBox[List["5", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]]]], "+", RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "18"]], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["3", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["9", " ", RowBox[List["Sin", "[", RowBox[List["5", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]]]], RowBox[List["3600", " ", SuperscriptBox["a", "2"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2002-12-18