Roboguru

H a s i l space d a r i space integral fraction numerator 4 x minus 8 over denominator square root of x squared minus 4 x plus 5 end root end fraction d x equals...

  1. 4 square root of x squared minus 4 x plus 5 end root plus C

  2. 2 square root of x squared minus 4 x plus 5 end root plus C

  3. 3 over 2 square root of x squared minus 4 x plus 5 end root plus C

  4. negative 3 over 2 square root of x squared minus 4 x plus 5 end root plus C

  5. negative 4 square root of x squared minus 4 x plus 5 end root plus C

Jawaban:

u equals x squared minus 4 x plus 5  fraction numerator d u over denominator d x end fraction equals 2 x minus 4 rightwards double arrow d x equals fraction numerator d u over denominator left parenthesis 2 x minus 4 right parenthesis end fraction  integral fraction numerator left parenthesis 4 x minus 8 right parenthesis over denominator square root of x squared minus 4 x plus 5 end root end fraction d x  equals integral fraction numerator left parenthesis 4 x minus 8 right parenthesis over denominator square root of u end fraction space fraction numerator d u over denominator 2 x minus 4 end fraction  equals integral fraction numerator 2 over denominator square root of u end fraction d u  equals 2 integral u to the power of negative 1 half end exponent d u  equals 4 u to the power of negative 1 half end exponent plus C  equals 4 square root of x squared minus 4 x plus 5 end root plus C

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