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Tentukan nilai ∫ x 2 x ​ x 2 − 4 x + 10 ​ d x

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M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

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begin mathsize 14px style integral fraction numerator x squared minus 4 x plus 10 over denominator x squared square root of x end fraction text d end text x end stylebegin mathsize 14px style equals integral fraction numerator x squared over denominator x squared square root of x end fraction d x minus integral fraction numerator 4 x over denominator x squared square root of x end fraction d x plus integral fraction numerator 10 over denominator x squared square root of x end fraction d x end style

                                  begin mathsize 14px style equals integral fraction numerator 1 over denominator square root of x end fraction d x minus 4 integral fraction numerator 1 over denominator x square root of x end fraction d x plus 10 integral fraction numerator 1 over denominator x squared square root of x end fraction d x equals integral fraction numerator 1 over denominator square root of x end fraction d x minus 4 integral fraction numerator 1 over denominator square root of x cubed end root end fraction d x plus 10 integral fraction numerator 1 over denominator square root of x to the power of 5 end root end fraction d x equals integral x to the power of negative 1 half end exponent d x minus 4 integral x to the power of negative 3 over 2 end exponent plus 10 integral x to the power of negative 5 over 2 end exponent d x end style

                                   size 14px equals fraction numerator size 14px 1 over denominator size 14px minus begin mathsize 14px display style 1 half end style size 14px plus size 14px 1 end fraction size 14px x to the power of size 14px minus size 14px 1 over size 14px 2 size 14px plus size 14px 1 end exponent size 14px minus fraction numerator 4 over denominator size 14px minus begin mathsize 14px display style 3 over 2 end style size 14px plus size 14px 1 end fraction size 14px x to the power of size 14px minus size 14px 3 over size 14px 2 size 14px plus size 14px 1 end exponent size 14px plus fraction numerator size 14px 10 over denominator size 14px minus begin mathsize 14px display style 5 over 2 end style size 14px plus size 14px 1 end fraction size 14px x to the power of size 14px minus size 14px 5 over size 14px 2 size 14px plus size 14px 1 end exponent size 14px plus size 14px C size 14px equals fraction numerator size 14px 1 over denominator begin mathsize 14px display style 1 half end style end fraction size 14px x to the power of size 14px 1 over size 14px 2 end exponent size 14px minus fraction numerator 4 over denominator begin mathsize 14px display style negative 1 half end style end fraction size 14px x to the power of size 14px minus size 14px 1 over size 14px 2 end exponent size 14px plus fraction numerator size 14px 10 over denominator begin mathsize 14px display style negative 3 over 2 end style end fraction size 14px x to the power of size 14px minus size 14px 3 over size 14px 2 end exponent size 14px plus size 14px C size 14px equals size 14px 2 size 14px x to the power of size 14px 1 over size 14px 2 end exponent size 14px minus size 14px 4 begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px x to the power of size 14px minus size 14px 1 over size 14px 2 end exponent size 14px plus size 14px 10 begin mathsize 14px style left parenthesis negative 2 over 3 right parenthesis end style size 14px x to the power of size 14px minus size 14px 3 over size 14px 2 end exponent size 14px plus size 14px C size 14px equals size 14px 2 square root of size 14px x size 14px plus fraction numerator size 14px 8 over denominator square root of size 14px x end fraction size 14px minus fraction numerator size 14px 20 over denominator size 14px 3 square root of size 14px x to the power of size 14px 3 end root end fraction size 14px plus size 14px C size 14px equals size 14px 2 square root of size 14px x size 14px plus fraction numerator size 14px 8 over denominator square root of size 14px x end fraction size 14px minus fraction numerator size 14px 20 over denominator size 14px 3 size 14px x square root of size 14px x end fraction size 14px plus size 14px C

                                  

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