integral of a^{ny}

解答

\int a^{n y} d y

\frac{a ^{n y}}{n ln ( a )} + C

求解步骤

\int a^{n y} d y

使用换元积分法

= \int \frac{a ^{u}}{n} d u

提出常数:

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

= \frac{1}{n} \cdot \int a^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{1}{n} \cdot \frac{a ^{u}}{ln ( a )}

u = n y

代回

= \frac{1}{n} \cdot \frac{a ^{n y}}{ln ( a )}

化简

\frac{1}{n} \cdot \frac{a ^{n y}}{ln ( a )} : \frac{a ^{n y}}{n ln ( a )}

= \frac{a ^{n y}}{n ln ( a )}

解答补常数

= \frac{a ^{n y}}{n ln ( a )} + C

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