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Pertanyaan

Hasil dari ∫ x ​ sin 4 ( 3 x ​ + 2 ) cos ( 3 x ​ + 2 ) ​ d x = ...

Hasil dari    

  1. begin mathsize 14px style 2 over 15 sin to the power of 5 space open parentheses 3 square root of x plus 2 close parentheses plus straight C end style  

  2. begin mathsize 14px style 1 over 15 sin to the power of 5 space open parentheses 3 square root of x plus 2 close parentheses plus straight C end style  

  3. begin mathsize 14px style negative 2 over 15 sin to the power of 5 space open parentheses 3 square root of x plus 2 close parentheses plus straight C end style 

  4. begin mathsize 14px style negative 1 over 15 sin to the power of 5 space open parentheses 3 square root of x plus 2 close parentheses plus straight C end style 

  5. begin mathsize 14px style negative 3 over 5 cos to the power of 5 space open parentheses 3 square root of x plus 2 close parentheses plus straight C end style 

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M. Nizar

Master Teacher

Mahasiswa/Alumni Universitas Siliwangi

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

jawaban yang tepat adalah A.

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Pembahasan

Misalkan : maka misalkan : Sehingga Jadi, jawaban yang tepat adalah A.

Misalkanspace:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row t equals cell 3 square root of x plus 2 end cell row cell straight d t end cell equals cell 3 times 1 half times x to the power of negative 1 half end exponent straight d x end cell row cell straight d t end cell equals cell fraction numerator 3 over denominator 2 square root of x end fraction straight d x end cell row cell straight d x end cell equals cell fraction numerator 2 square root of x over denominator 3 end fraction straight d t end cell end table end style

makaundefined 

begin mathsize 14px style integral fraction numerator sin to the power of 4 space t space cos space t over denominator up diagonal strike square root of x end strike end fraction times fraction numerator 2 up diagonal strike square root of x end strike over denominator 3 end fraction straight d t equals 2 over 3 integral sin to the power of 4 space t space cos space t space straight d t end style

misalkanundefined:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell sin space t end cell row cell straight d u end cell equals cell cos space t space straight d t end cell end table end style

Sehinggaundefined

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 over 3 integral sin to the power of 4 space t space cos space t space straight d t end cell equals cell 2 over 3 integral u to the power of 4 straight d u end cell row blank equals cell 2 over 3 times 1 fifth u to the power of 5 plus C end cell row blank equals cell 2 over 15 sin to the power of 5 t plus C end cell row blank equals cell 2 over 15 sin to the power of 5 open parentheses 3 square root of x plus 2 close parentheses plus C end cell end table end style

Jadi, jawaban yang tepat adalah A.

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