integral of (sin(2t))/(sin(t))

解答

\int \frac{sin ( 2 t )}{sin ( t )} d t

2 sin (t) + C

求解步骤

\int \frac{sin ( 2 t )}{sin ( t )} d t

使用三角恒等式改写

= \int 2 cos (t) d t

提出常数:

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

= 2 \cdot \int cos (t) d t

使用积分常见定则:

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

= 2 sin (t)

解答补常数

= 2 sin (t) + C

\int 2 cos (x) - 9 sin (x) d x

\int 3 x^{\frac{4}{3}} d x

\int x + \frac{2}{x} d x

\int 3 e^{x} + 4 d x

\int (2 x + 1) \cdot cos (4 x) d x