integral of t^3e^{-t^4}

解答

\int t^{3} e^{- t^{4}} d t

- \frac{1}{4} e^{- t^{4}} + C

求解步骤

\int t^{3} e^{- t^{4}} d t

使用换元积分法

= \int - \frac{e ^{u}}{4} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{4} \cdot \int e^{u} d u

使用积分常见定则:

\int e^{u} d u = e^{u}

= - \frac{1}{4} e^{u}

u = - t^{4}

代回

= - \frac{1}{4} e^{- t^{4}}

解答补常数

= - \frac{1}{4} e^{- t^{4}} + C

x \to 0 lim (x^{2} cos (\frac{5}{x}))

8 x^{2} y + y^{^{'}} = - 3 x^{2}

\frac{d}{d x} (x^{\frac{1}{2}} y)

r \cdot \frac{d q}{d r} + 3 q = 0

x \to 0 + lim (5 x + 6)