Pertanyaan

∫ − 1 2 x + 2 x − 1 dx = …

$\int_{- 1}^{2} \frac{x - 1}{x + 2} dx = \dots$

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N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

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$begin mathsize 14px style integral subscript negative 1 end subscript superscript 2 fraction numerator straight x minus 1 over denominator square root of straight x plus 2 end root end fraction dx integral subscript 1 superscript 4 fraction numerator straight u minus 2 minus 1 over denominator square root of straight u end fraction du integral subscript 1 superscript 4 square root of straight u minus fraction numerator 3 over denominator square root of straight u end fraction du integral subscript 1 superscript 4 open parentheses straight u to the power of 1 half end exponent minus 3 straight u to the power of negative 1 half end exponent close parentheses du 2 over 3 straight u to the power of 3 over 2 end exponent minus 6 straight u to the power of 1 half end exponent open table row 4 row 1 end table close square brackets open parentheses 2 over 3 open parentheses 4 close parentheses to the power of 3 over 2 end exponent minus 6 open parentheses 4 close parentheses to the power of 1 half end exponent close parentheses minus open parentheses 2 over 3 open parentheses 1 close parentheses to the power of 3 over 2 end exponent minus 6 open parentheses 1 close parentheses to the power of 1 half end exponent close parentheses open parentheses 2 over 3 open parentheses 8 close parentheses minus 12 close parentheses minus open parentheses 2 over 3 minus 6 close parentheses 16 over 3 minus 12 minus 2 over 3 plus 6 equals 14 over 3 minus 6 equals negative 4 over 3 end style$