integral of e^{6x+7}

解答

\int e^{6 x + 7} d x

\frac{1}{6} e^{6 x + 7} + C

求解步骤

\int e^{6 x + 7} d x

使用换元积分法

= \int e^{u} \frac{1}{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 = 6 x + 7

代回

= \frac{1}{6} e^{6 x + 7}

解答补常数

= \frac{1}{6} e^{6 x + 7} + C

t an g e n t \frac{3}{1 + x ^{2}}

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