maclaurin e^{x^3}

Lösung

maclaurin

e^{x^{3}}

1 + x^{3} + \frac{1}{2} x^{6} + \frac{1}{6} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{360}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{60480}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= 1 + x^{3} + \frac{1}{2} x^{6} + \frac{1}{6} x^{9} + \dots

\int \frac{1}{( 1 + x )} d x

y^{^{''}} = y^{^{'}} + 2 y + 9 e^{2 x}

\int 11 sin^{2} (x co) s^{2} x d x

\int 2 x^{3} e^{- x^{2}} d x

(x^{2} - 2 y^{2}) d y - 2 x y d x = 0