What is taylor 3ln(1+2x^2) ?

The answer to taylor 3ln(1+2x^2) is 6x^2-6x^4+8x^6-12x^8+96/5 x^{10}+\ldots

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taylor 3ln(1+2x^2)

taylor

3 ln (1 + 2 x^{2})

6 x^{2} - 6 x^{4} + 8 x^{6} - 12 x^{8} + \frac{96}{5} x^{10} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{12}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 144}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{5760}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 483840}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{69672960}{10 !} x^{10} + \dots

Refine

= 6 x^{2} - 6 x^{4} + 8 x^{6} - 12 x^{8} + \frac{96}{5} x^{10} + \dots

\int \frac{16 + x ^{2}}{x} d x

\int_{2}^{\infty} y e^{- 4 y} d y

\int arcsin (7 x) d x

\frac{d}{d x} (arctan (\frac{π}{x}))

\frac{1}{tan ( x )}

What is taylor 3ln(1+2x^2) ?
The answer to taylor 3ln(1+2x^2) is 6x^2-6x^4+8x^6-12x^8+96/5 x^{10}+\ldots