integral of cos(3x+4)

解答

\int cos (3 x + 4) d x

\frac{1}{3} sin (3 x + 4) + C

求解步骤

\int cos (3 x + 4) d x

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 x + 4

代回

= \frac{1}{3} sin (3 x + 4)

解答补常数

= \frac{1}{3} sin (3 x + 4) + C

\frac{d}{d x} (\frac{a}{x ^{b}})

n = 0 \sum \infty \frac{1}{2 ^{2 n - 1}}

\int_{0}^{a} \frac{1}{( a + r - x ) ^{2}} d x

\frac{d}{d x} (5 x^{6} - 12)

\int e^{5 x} cos (8 x) d x