integral of x^5e^{-x^6}

解答

\int x^{5} e^{- x^{6}} d x

- \frac{1}{6} e^{- x^{6}} + C

求解步骤

\int x^{5} e^{- x^{6}} d x

使用换元积分法

= \int - \frac{e ^{u}}{6} d u

提出常数:

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

= - \frac{1}{6} \cdot \int e^{u} d u

使用积分常见定则:

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

= - \frac{1}{6} e^{u}

u = - x^{6}

代回

= - \frac{1}{6} e^{- x^{6}}

解答补常数

= - \frac{1}{6} e^{- x^{6}} + C

x + y (\frac{d y}{d x}) = 0

\int (x x + 6) d x

\int 7 cos (θ) cos^{5} (sin (θ)) d θ

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