integral of sec^2(2t)

解答

\int sec^{2} (2 t) d t

\frac{1}{2} tan (2 t) + C

求解步骤

\int sec^{2} (2 t) d t

使用换元积分法

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

提出常数:

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

= \frac{1}{2} \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}{2} tan (u)

u = 2 t

代回

= \frac{1}{2} tan (2 t)

解答补常数

= \frac{1}{2} tan (2 t) + C