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Hasil ∫ ( x + 5 ) 4 − 3 x ​ d x = ...

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

 integral open parentheses x plus 5 close parentheses square root of 4 minus 3 x end root d x equals negative 38 over 27 open parentheses 4 minus 3 x close parentheses to the power of 3 over 2 end exponent plus 2 over 45 open parentheses 4 minus 3 x close parentheses to the power of 5 over 2 end exponent equals C. 

Pembahasan

Misalnya Maka Sehingga Jadi, .

Misalnya 

u equals 4 minus 3 x

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell d u end cell equals cell d open parentheses 4 minus 3 x close parentheses end cell row cell d u end cell equals cell negative 3 d x end cell row cell d x end cell equals cell negative 1 third d u end cell row blank blank blank row u equals cell 4 minus 3 x end cell row cell 3 x end cell equals cell 4 minus u end cell row x equals cell 4 over 3 minus u over 3 end cell end table 

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses x plus 5 close parentheses square root of 4 minus 3 x end root d x end cell equals cell integral open parentheses open parentheses 4 over 3 minus u over 3 close parentheses plus 5 close parentheses square root of u open parentheses negative 1 third d u close parentheses end cell row blank equals cell negative 1 third integral open parentheses 19 over 3 minus u over 3 close parentheses square root of u d u end cell row blank equals cell negative 1 over 9 integral open parentheses 19 minus u close parentheses square root of u d u end cell row blank equals cell negative 1 over 9 integral open parentheses 19 square root of u minus u square root of u close parentheses d u end cell row blank equals cell negative 1 over 9 integral open parentheses 19 u to the power of 1 half end exponent minus u to the power of 3 over 2 end exponent close parentheses d u end cell row blank equals cell negative 1 over 9 open parentheses 19 times 2 over 3 u to the power of 3 over 2 end exponent minus 2 over 5 u to the power of 5 over 2 end exponent close parentheses plus C end cell row blank equals cell negative 38 over 27 u to the power of 3 over 2 end exponent plus 2 over 45 u to the power of 5 over 2 end exponent plus C end cell row blank equals cell negative 38 over 27 open parentheses 4 minus 3 x close parentheses to the power of 3 over 2 end exponent plus 2 over 45 open parentheses 4 minus 3 x close parentheses to the power of 5 over 2 end exponent plus C end cell end table 

Jadi, integral open parentheses x plus 5 close parentheses square root of 4 minus 3 x end root d x equals negative 38 over 27 open parentheses 4 minus 3 x close parentheses to the power of 3 over 2 end exponent plus 2 over 45 open parentheses 4 minus 3 x close parentheses to the power of 5 over 2 end exponent equals C. 

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