integral of xe^{ax}

解答

\int x e^{a x} d x

e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}} + C

求解步骤

\int x e^{a x} d x

使用分布积分法

= e^{a x} \frac{1}{a} x - \int e^{a x} \frac{1}{a} d x

\int e^{a x} \frac{1}{a} d x = e^{a x} \frac{1}{a ^{2}}

= e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}}

解答补常数

= e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}} + C

2 y^{^{''}} - 3 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = \frac{1}{2}

\int t^{2} t + 8 d t

d er i v a t i v e y = \frac{2 x}{x - 1}

x \to 0 lim ((\frac{2 arccos ( x )}{π})^{\frac{1}{x}})

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