What is maclaurin arctan(5x) ?

The answer to maclaurin arctan(5x) is 5x-125/3 x^3+625x^5-78125/7 x^7+1953125/9 x^9+\ldots

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maclaurin arctan(5x)

maclaurin

arctan (5 x)

5 x - \frac{125}{3} x^{3} + 625 x^{5} - \frac{78125}{7} x^{7} + \frac{1953125}{9} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{5}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 250}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{75000}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 56250000}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{78750000000}{9 !} x^{9} + \dots

Refine

= 5 x - \frac{125}{3} x^{3} + 625 x^{5} - \frac{78125}{7} x^{7} + \frac{1953125}{9} x^{9} + \dots

\frac{d}{d t} (- 2 e^{- t^{2}} t)

\int \frac{2}{( x - 2 ) ( x ^{2} + 4 )} d x

\int cos^{2} (z) sin^{4} (z) d z

\int (\frac{x}{5})^{2} d x

\frac{d}{d x} (- 3 cos (x) + 2 sin (x))

What is maclaurin arctan(5x) ?
The answer to maclaurin arctan(5x) is 5x-125/3 x^3+625x^5-78125/7 x^7+1953125/9 x^9+\ldots