integral of sin(2x)e^{cos^2(x)}

解答

\int sin (2 x) e^{c o s^{2} (x)} d x

- e^{c o s^{2} (x)} + C

求解步骤

\int sin (2 x) e^{c o s^{2} (x)} d x

使用换元积分法

= \int - 1 d u

常数积分:

\int a d x = a x

= (- 1) u

u = e^{c o s^{2} (x)}

代回

= (- 1) e^{c o s^{2} (x)}

化简

= - e^{c o s^{2} (x)}

解答补常数

= - e^{c o s^{2} (x)} + C

x \to 3 lim (\frac{6}{x - 3})

d er i v a t i v e 2 x - 3

x \to - 1 - lim (\frac{1}{x + 1})

\frac{d y}{d x} + y = x y^{8}

d er i v a t i v e f (x) = 5 x + 2