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Selesaikanlah integral ∫x2x2−3​dx

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Selesaikanlah integral begin mathsize 14px style integral fraction numerator x squared minus 3 over denominator x squared end fraction text d end text x end style 

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F. Ayudhita

Master Teacher

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Pembahasan

begin mathsize 14px style integral fraction numerator x squared minus 3 over denominator x squared end fraction text d end text x end styleequals integral size 14px x to the power of size 14px 2 over size 14px x to the power of size 14px 2 size 14px d size 14px x size 14px minus integral size 14px 3 over size 14px x to the power of size 14px 2 size 14px d size 14px x 

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

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