integral of (e^{6/x})/(x^2)

解答

\int \frac{e ^{\frac{6}{x}}}{x ^{2}} d x

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

求解步骤

\int \frac{e ^{\frac{6}{x}}}{x ^{2}} 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 = \frac{6}{x}

代回

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

解答补常数

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

\int \frac{1}{s} d s

\int \frac{cosh ( x )}{2 + 3 sinh ( x )} d x

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