taylor x^n

Solution

taylor

x^{n}

\dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= \dots

\int \frac{3 x ^{2} + x + 1}{x ^{2} - 2 x + 5} d x

arctan (\frac{2}{x})

x^{2} y^{^{''}} + y^{^{'}} = 0

\int_{0}^{1} x^{6} (1 + 2 x^{7})^{5} d x

f (x) = x^{4} sec (5 x)