Pertanyaan

Selesaikanlah integral ∫ x 3 x 9 − 3 d x

Selesaikanlah integral $\int \frac{x ^{9} - 3}{x ^{3}} d x$

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Klaim

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style integral fraction numerator x to the power of 9 minus 3 over denominator x cubed end fraction text d end text x end style$

$begin mathsize 14px style equals integral x to the power of 6 space d x space minus space integral 3 x to the power of negative 3 end exponent space d x equals fraction numerator 1 over denominator 6 plus 1 end fraction x to the power of 6 plus 1 end exponent minus fraction numerator 3 over denominator negative 3 plus 1 end fraction x to the power of negative 3 plus 1 end exponent plus C equals 1 over 7 x to the power of 7 minus fraction numerator 3 over denominator negative 2 end fraction x to the power of negative 2 end exponent plus C equals 1 over 7 x to the power of 7 plus 3 over 2 x to the power of negative 2 end exponent plus C end style$

$begin mathsize 14px style equals 1 over 7 x to the power of 7 plus fraction numerator 3 over denominator 2 x squared end fraction plus C end style$