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受欢迎的微积分 >

integral of (sqrt(9-w^2))/(w^2)

解答

\int \frac{9 - w ^{2}}{w ^{2}} d w

解答

- arcsin (\frac{1}{3} w) - \frac{9 - w ^{2}}{w} + C

求解步骤

\int \frac{9 - w ^{2}}{w ^{2}} d w

使用三角换元法

= \int cot^{2} (u) d u

使用三角恒等式改写

= \int - 1 + csc^{2} (u) d u

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1 d u + \int csc^{2} (u) d u

\int 1 d u = u

\int csc^{2} (u) d u = - cot (u)

= - u - cot (u)

u = arcsin (\frac{1}{3} w)

代回

= - arcsin (\frac{1}{3} w) - cot (arcsin (\frac{1}{3} w))

化简

- arcsin (\frac{1}{3} w) - cot (arcsin (\frac{1}{3} w)) : - arcsin (\frac{1}{3} w) - \frac{9 - w ^{2}}{w}

= - arcsin (\frac{1}{3} w) - \frac{9 - w ^{2}}{w}

解答补常数

= - arcsin (\frac{1}{3} w) - \frac{9 - w ^{2}}{w} + C

作图

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\frac{d}{d y} (0)

\frac{d v}{d t} = - v

integral of sh x/3

\int s h \frac{x}{3} d x

integral of 29arctan(sqrt(x))

\int 29 arctan (x) d x

derivative of e^{2x-3}

\frac{d}{d x} (e^{2 x - 3})