What is maclaurin ln((sqrt(1+2x))/(1-3x)) ?

The answer to maclaurin ln((sqrt(1+2x))/(1-3x)) is 4x+7/2 x^2+31/3 x^3+73/4 x^4+259/5 x^5+\ldots

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maclaurin ln((sqrt(1+2x))/(1-3x))

maclaurin

ln (\frac{1 + 2 x}{1 - 3 x})

4 x + \frac{7}{2} x^{2} + \frac{31}{3} x^{3} + \frac{73}{4} x^{4} + \frac{259}{5} x^{5} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{4}{1 !} x + \frac{7}{2 !} x^{2} + \frac{62}{3 !} x^{3} + \frac{438}{4 !} x^{4} + \frac{6216}{5 !} x^{5} + \dots

Refine

= 4 x + \frac{7}{2} x^{2} + \frac{31}{3} x^{3} + \frac{73}{4} x^{4} + \frac{259}{5} x^{5} + \dots

(4.5) (1.2)

\frac{d}{d x} (\frac{x ^{3}}{sin ( x )})

y = x^{2} - 2 x + 3, (2, 3)

\frac{\partial}{\partial x} (7 x)

\frac{( x ^{2} + 1 ) d y}{d x} + 7 x (y - 1) = 0

What is maclaurin ln((sqrt(1+2x))/(1-3x)) ?
The answer to maclaurin ln((sqrt(1+2x))/(1-3x)) is 4x+7/2 x^2+31/3 x^3+73/4 x^4+259/5 x^5+\ldots