What is taylor (x^2+9)^{-3} ?

The answer to taylor (x^2+9)^{-3} is 1/729-1/2187 x^2+2/19683 x^4-10/531441 x^6+5/1594323 x^8+\ldots

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taylor (x^2+9)^{-3}

taylor

(x^{2} + 9)^{- 3}

\frac{1}{729} - \frac{1}{2187} x^{2} + \frac{2}{19683} x^{4} - \frac{10}{531441} x^{6} + \frac{5}{1594323} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{729} + \frac{\frac{d}{d x} ( ( x ^{2} + 9 ) ^{- 3} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x ^{2} + 9 ) ^{- 3} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x ^{2} + 9 ) ^{- 3} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{729} + \frac{0}{1 !} x + \frac{- \frac{2}{2187}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{16}{6561}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{800}{59049}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{3968092800}{9 ^{11}}}{8 !} x^{8} + \dots

Refine

= \frac{1}{729} - \frac{1}{2187} x^{2} + \frac{2}{19683} x^{4} - \frac{10}{531441} x^{6} + \frac{5}{1594323} x^{8} + \dots

\frac{d}{d x} (x sec^{2} (π x))

x \to - 0 lim (2 x e^{2 x} + k x)

\int 1 + \frac{2}{t} d t

\int cot (17 x) d x

\int (cos (x) + \frac{1}{3} x) d x

What is taylor (x^2+9)^{-3} ?
The answer to taylor (x^2+9)^{-3} is 1/729-1/2187 x^2+2/19683 x^4-10/531441 x^6+5/1594323 x^8+\ldots