Selesaikanlah integral ∫x3x9−3​dx

Pertanyaan

Selesaikanlah integral 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 

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F. Ayudhita

Master Teacher

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Pembahasan

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 open parentheses x to the power of 9 over x cubed minus 3 over x cubed close parentheses d 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

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Irma Mardiana

Makasih ❤️

Rahel Simbolon

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Tunjukkan bahwa untuk t<2 selalu berlaku: ∫[1+(t−1)+(t−1)2+(t−1)3+… +3mu]dt=ln∣∣​2−t1​∣∣​+C

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