integral of 1/(arcsin(x)sqrt(1-x^2))

解答

\int \frac{1}{arcsin ( x ) 1 - x ^{2}} d x

ln ∣ arcsin (x) ∣ + C

求解步骤

\int \frac{1}{arcsin ( x ) 1 - x ^{2}} d x

使用换元积分法

= \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

u = arcsin (x)

代回

= ln ∣ arcsin (x) ∣

解答补常数

= ln ∣ arcsin (x) ∣ + C

\frac{\partial}{\partial x} (x^{2} + x y + y^{2} + 2 x - y)

\frac{d}{d t} (- cos (2 t))

\int (2 x^{4} - 8 x^{3}) \cdot e^{- 3 x} d x

(2 x y) d y + (x^{2} + y^{2}) d x = 0

d er i v a t i v e y = (tan (x))^{\frac{9}{x}}