integral of cos(2*x)

解答

\int cos (2 \cdot x) d x

\frac{1}{2} sin (2 x) + C

求解步骤

\int cos (2 x) d x

使用换元积分法

= \int cos (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 cos (u) d u

使用积分常见定则:

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

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

u = 2 x

代回

= \frac{1}{2} sin (2 x)

解答补常数

= \frac{1}{2} sin (2 x) + C

\int sin (tan (x)) d x

\int \frac{x + 1}{x - 1} d x

\int e^{e^{e^{x}}} d e^{e^{x}}

\int \frac{1}{2 + cos ^{2} ( x )} d x

\int 2 sin (x) - 2 x^{\frac{5}{2}} + C d x