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受欢迎的微积分 >

integral of sec^2(5x-1)

解答

\int sec^{2} (5 x - 1) d x

解答

- \frac{1}{5} tan (1 - 5 x) + C

求解步骤

\int sec^{2} (5 x - 1) d x

因式分解

5 x - 1 : - (- 5 x + 1)

= \int sec^{2} (- (- 5 x + 1)) d x

化简

sec^{2} (- (- 5 x + 1)) : sec^{2} (1 - 5 x)

= \int sec^{2} (1 - 5 x) d x

使用换元积分法

= \int - \frac{1}{5} sec^{2} (u) d u

提出常数:

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

= - \frac{1}{5} \cdot \int sec^{2} (u) d u

使用积分常见定则:

\int sec^{2} (u) d u = tan (u)

= - \frac{1}{5} tan (u)

u = 1 - 5 x

代回

= - \frac{1}{5} tan (1 - 5 x)

解答补常数

= - \frac{1}{5} tan (1 - 5 x) + C

作图

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