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受欢迎的微积分 >

integral of (sin(x))/(sqrt(2-cos^2(x)))

解答

\int \frac{sin ( x )}{2 - cos ^{2} ( x )} d x

解答

- arcsin (\frac{1}{2} cos (x)) + C

求解步骤

\int \frac{sin ( x )}{2 - cos ^{2} ( x )} d x

使用换元积分法

= \int - \frac{1}{2 - u ^{2}} d u

提出常数:

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

= - \int \frac{1}{2 - u ^{2}} d u

使用三角换元法

= - \int 1 d v

常数积分:

\int a d x = a x

= - 1 \cdot v

代回

= - 1 \cdot arcsin (\frac{1}{2} cos (x))

化简

= - arcsin (\frac{1}{2} cos (x))

解答补常数

= - arcsin (\frac{1}{2} cos (x)) + C

作图

流行的例子

derivative e^{4x}cos(7x)

d er i v a t i v e e^{4 x} cos (7 x)

derivative of 120x

\frac{d}{d x} (120 x)

limit as x approaches 0 of (4x^2-3x)/(x^2+0.8x+4/x)

x \to 0 lim (\frac{4 x ^{2} - 3 x}{x ^{2} + 0.8 x + \frac{4}{x}})

(d^2)/(dx^2)(sqrt(r)+\sqrt[3]{r})

\frac{d ^{2}}{d x ^{2}} (r + 3 r)

derivative ((x+8)/(x-8))^5

d er i v a t i v e (\frac{x + 8}{x - 8})^{5}