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Hasil dari ∫ ( 2 x − 1 ) x 2 − x + 5 d x adalah... (UN 2013)

Hasil dari $\int (2 x - 1) x^{2} - x + 5 d x$ adalah... (UN 2013)

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$Misal colon u equals x squared minus x plus 5 d u equals 2 x minus 1 d x left right double arrow d x equals fraction numerator d u over denominator 2 x minus 1 end fraction Maka integral left parenthesis up diagonal strike 2 x minus 1 right parenthesis end strike square root of u fraction numerator d u over denominator up diagonal strike 2 x minus 1 end strike end fraction integral square root of u space d u equals integral u to the power of bevelled 1 half end exponent space d u space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator begin display style 1 half end style plus 1 end fraction times U to the power of 1 half plus 1 end exponent plus C space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction U to the power of 3 over 2 end exponent plus C space space space space space space space space space space space space space space space space equals 2 over 3 U to the power of 3 over 2 end exponent plus C space space space space space space space space space space space space space space space space equals 2 over 3 left parenthesis x squared minus x plus 5 right parenthesis to the power of 3 over 2 end exponent plus C space space space space space space space space space space space space space space space space equals 2 over 3 left parenthesis x squared minus x plus 5 right parenthesis left parenthesis x squared minus x plus 5 right parenthesis to the power of 1 half end exponent plus C space space space space space space space space space space space space space space space space equals 2 over 3 left parenthesis x squared minus x plus 5 right parenthesis square root of x squared minus x plus 5 end root plus C$