Pertanyaan

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

Tentukan nilai $\int \frac{x ^{2} - 4 x + 10}{x ^{2} x} d x$

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Habis dalam

Klaim

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

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

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

$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$