maclaurin x^3e^{2x}

Lösung

maclaurin

x^{3} e^{2 x}

x^{3} + 2 x^{4} + 2 x^{5} + \frac{4}{3} x^{6} + \frac{2}{3} x^{7} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \frac{240}{5 !} x^{5} + \frac{960}{6 !} x^{6} + \frac{3360}{7 !} x^{7} + \dots

Fasse zusammen

= x^{3} + 2 x^{4} + 2 x^{5} + \frac{4}{3} x^{6} + \frac{2}{3} x^{7} + \dots

n = 0 \sum \infty \frac{x ^{n}}{3 \cdot n}

d er i v a t i v e y = \frac{3}{x}

y^{^{'}} = 3 x^{2} e^{- y}

\int \frac{1}{x ln ( x ^{6} )} d x

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