حمّل تطبيق منهاجي الجديد

منهاجي صار أسرع من خلال التطبيق

  إجابات كتاب التمارين

إجابات كتاب التمارين

تكامل اقترانات خاصة

أجد كلاً من التكاملات الآتية:

(1) begin mathsize 20px style integral 4 e to the power of negative 5 x end exponent space d x end style

begin mathsize 20px style integral 4 e to the power of negative 5 x space end exponent d x equals negative 4 over 5 e to the power of negative 5 x end exponent plus C end style

(2) begin mathsize 20px style integral left parenthesis sin invisible function application space 2 x minus cos invisible function application space 2 x right parenthesis space d x end style

begin mathsize 20px style integral left parenthesis sin invisible function application space 2 x minus cos invisible function application space 2 x right parenthesis space d x equals negative 1 half cos invisible function application space 2 x minus 1 half sin invisible function application space 2 x plus C end style

(3) begin mathsize 20px style integral cos squared invisible function application space 2 x space d x end style

begin mathsize 20px style integral cos squared invisible function application space 2 x space d x equals 1 half integral left parenthesis 1 plus cos invisible function application space 4 x right parenthesis space d x equals 1 half x plus 1 over 8 sin invisible function application space 4 x plus C end style

(4) begin mathsize 20px style integral fraction numerator e to the power of x plus 4 over denominator e to the power of 2 x end exponent end fraction space d x end style

begin mathsize 20px style integral fraction numerator e to the power of x plus 4 over denominator e to the power of 2 x end exponent end fraction space d x equals integral left parenthesis e to the power of negative x end exponent plus 4 e to the power of negative 2 x end exponent right parenthesis space d x equals negative e to the power of negative x end exponent minus 2 e to the power of negative 2 x end exponent plus C end style

(5) begin mathsize 20px style integral left parenthesis fraction numerator cos invisible function application space x over denominator sin squared invisible function application space x end fraction minus 2 e to the power of x right parenthesis space d x end style

begin mathsize 20px style integral left parenthesis cot invisible function application space x csc invisible function application space x minus 2 e to the power of x right parenthesis space d x equals negative csc invisible function application space x minus 2 e to the power of x plus C end style

(6) begin mathsize 20px style integral left parenthesis 3 cos invisible function application space 3 x minus tan squared invisible function application space x right parenthesis space d x end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell integral left parenthesis 3 cos invisible function application space 3 x minus tan squared invisible function application space x right parenthesis space d x end cell cell equals integral left parenthesis 3 cos invisible function application space 3 x minus left parenthesis sec squared invisible function application space x minus 1 right parenthesis right parenthesis space d x end cell row blank cell equals sin invisible function application space 3 x minus tan invisible function application space x plus x plus C end cell end table end style

(7) begin mathsize 20px style integral cos invisible function application space x left parenthesis 1 plus csc squared invisible function application space x right parenthesis space d x end style

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إعداد : شبكة منهاجي التعليمية

10 / 07 / 2023

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