integral of e^{tan(31x)}sec^2(31x)

解答

\int e^{t a n (31 x)} sec^{2} (31 x) d x

\frac{1}{31} e^{t a n (31 x)} + C

求解步骤

\int e^{t a n (31 x)} sec^{2} (31 x) d x

使用换元积分法

= \int e^{t a n (u)} sec^{2} (u) \frac{1}{31} d u

提出常数:

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

= \frac{1}{31} \cdot \int e^{t a n (u)} sec^{2} (u) d u

使用换元积分法

= \frac{1}{31} \cdot \int e^{v} d v

使用积分常见定则:

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

= \frac{1}{31} e^{v}

代回

= \frac{1}{31} e^{t a n (31 x)}

解答补常数

= \frac{1}{31} e^{t a n (31 x)} + C

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