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

解答

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

arcsin^{2} (x) + C

求解步骤

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

提出常数:

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

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

使用换元积分法

= 2 \cdot \int u d u

使用幂法则

= 2 \cdot \frac{u ^{2}}{2}

u = arcsin (x)

代回

= 2 \cdot \frac{arcsin ^{2} ( x )}{2}

化简

2 \cdot \frac{arcsin ^{2} ( x )}{2} : arcsin^{2} (x)

= arcsin^{2} (x)

解答补常数

= arcsin^{2} (x) + C

y^{^{''}} + 36 y = 36 sin (6 x)

\int \frac{324 - x ^{2}}{x} d x

5 \frac{d y}{d t} + y = 20 t

\int e^{5 - 2 x} d x

\int cos (p i x) d x