maclaurin f(x)=(1+x)^{-5/3}

Lösung

maclaurin

f (x) = (1 + x)^{- \frac{5}{3}}

1 - \frac{5}{3} x + \frac{20}{9} x^{2} - \frac{220}{81} x^{3} + \frac{770}{243} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{- \frac{5}{3}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{- \frac{5}{3}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{- \frac{5}{3}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- \frac{5}{3}}{1 !} x + \frac{\frac{40}{9}}{2 !} x^{2} + \frac{- \frac{440}{27}}{3 !} x^{3} + \frac{\frac{6160}{81}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - \frac{5}{3} x + \frac{20}{9} x^{2} - \frac{220}{81} x^{3} + \frac{770}{243} x^{4} + \dots

\int x^{2} (6 x^{3} - 5)^{4} d x

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