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Nilai integral subscript 1 superscript 36 fraction numerator 3 over denominator square root of x left parenthesis 3 plus square root of x right parenthesis to the power of 3 divided by 2 end exponent end fractiondx adalah...

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

integral subscript 1 superscript 36 fraction numerator 3 over denominator square root of x open parentheses 3 plus square root of x close parentheses to the power of 3 over 2 end exponent end fraction d x  G u n a k a n space i n t e g r a l space s u b t i t u s i  u equals 3 plus square root of x  x equals 1 rightwards double arrow u equals 3 plus square root of 1 equals 4  x equals 36 rightwards double arrow u equals 3 plus square root of 36 equals 9  fraction numerator d u over denominator d x end fraction equals fraction numerator 1 over denominator 2 square root of x end fraction left right double arrow d x equals 2 square root of x space d u  integral subscript 1 superscript 36 fraction numerator 3 over denominator square root of x open parentheses 3 plus square root of x close parentheses to the power of 3 over 2 end exponent end fraction d x equals integral subscript 4 superscript 9 fraction numerator 3 over denominator square root of x open parentheses u close parentheses to the power of 3 over 2 end exponent end fraction 2 square root of x d u  integral subscript 4 superscript 9 6 u to the power of negative 3 over 2 end exponent d u  6. space open parentheses negative 2 close parentheses u to the power of negative 1 half end exponent open table row 9 row 4 end table close angle brackets  minus 12 open parentheses 9 to the power of negative 1 half end exponent minus 4 to the power of negative 1 half end exponent close parentheses  minus 12 open parentheses 1 third minus 1 half close parentheses  minus 12 open parentheses negative 1 over 6 close parentheses equals 2

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