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受欢迎的微积分 >

integral of 5sec^2(1+5x)

解答

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

解答

tan (1 + 5 x) + C

求解步骤

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

提出常数:

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

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

使用换元积分法

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

提出常数:

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

= 5 \cdot \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)

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

u = 1 + 5 x

代回

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

化简

5 \cdot \frac{1}{5} tan (1 + 5 x) : tan (1 + 5 x)

= tan (1 + 5 x)

解答补常数

= tan (1 + 5 x) + C

作图

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