integral of cos(3θ-1)

解答

\int cos (3 θ - 1) d θ

\frac{1}{3} sin (3 θ - 1) + C

求解步骤

\int cos (3 θ - 1) d θ

使用换元积分法

= \int cos (u) \frac{1}{3} d u

提出常数:

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

= \frac{1}{3} \cdot \int cos (u) d u

使用积分常见定则:

\int cos (u) d u = sin (u)

= \frac{1}{3} sin (u)

u = 3 θ - 1

代回

= \frac{1}{3} sin (3 θ - 1)

解答补常数

= \frac{1}{3} sin (3 θ - 1) + C

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