integral of 2/3 sec(v)tan(v)

解答

\int \frac{2}{3} sec (v) tan (v) d v

\frac{2}{3} sec (v) + C

求解步骤

\int \frac{2}{3} sec (v) tan (v) d v

提出常数:

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

= \frac{2}{3} \cdot \int sec (v) tan (v) d v

使用换元积分法

= \frac{2}{3} \cdot \int 1 d u

常数积分:

\int a d x = a x

= \frac{2}{3} \cdot 1 \cdot u

u = sec (v)

代回

= \frac{2}{3} \cdot 1 \cdot sec (v)

化简

= \frac{2}{3} sec (v)

解答补常数

= \frac{2}{3} sec (v) + C

\int e^{\frac{1}{6} x} d x

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