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受欢迎的微积分 >

integral of e^{tan(46x)}sec^2(46x)

解答

\int e^{t a n (46 x)} sec^{2} (46 x) d x

解答

\frac{1}{46} e^{t a n (46 x)} + C

求解步骤

\int e^{t a n (46 x)} sec^{2} (46 x) d x

使用换元积分法

= \int e^{t a n (u)} sec^{2} (u) \frac{1}{46} d u

提出常数:

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

= \frac{1}{46} \cdot \int e^{t a n (u)} sec^{2} (u) d u

使用换元积分法

= \frac{1}{46} \cdot \int e^{v} d v

使用积分常见定则:

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

= \frac{1}{46} e^{v}

代回

= \frac{1}{46} e^{t a n (46 x)}

解答补常数

= \frac{1}{46} e^{t a n (46 x)} + C

作图

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