What is taylor ln(1+12x) ?

The answer to taylor ln(1+12x) is 12x-72x^2+576x^3-5184x^4+248832/5 x^5+\ldots

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taylor ln(1+12x)

taylor

ln (1 + 12 x)

12 x - 72 x^{2} + 576 x^{3} - 5184 x^{4} + \frac{248832}{5} x^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( ln ( 1 + 12 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( 1 + 12 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( 1 + 12 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{12}{1 !} x + \frac{- 144}{2 !} x^{2} + \frac{3456}{3 !} x^{3} + \frac{- 124416}{4 !} x^{4} + \frac{5971968}{5 !} x^{5} + \dots

Refine

= 12 x - 72 x^{2} + 576 x^{3} - 5184 x^{4} + \frac{248832}{5} x^{5} + \dots

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What is taylor ln(1+12x) ?
The answer to taylor ln(1+12x) is 12x-72x^2+576x^3-5184x^4+248832/5 x^5+\ldots