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受欢迎的微积分 >

integral of (arcsin(3x))/(sqrt(1-9x^2))

解答

\int \frac{arcsin ( 3 x )}{1 - 9 x ^{2}} d x

解答

\frac{1}{6} arcsin^{2} (3 x) + C

求解步骤

\int \frac{arcsin ( 3 x )}{1 - 9 x ^{2}} d x

使用换元积分法

= \int \frac{arcsin ( u )}{3 1 - u ^{2}} d u

提出常数:

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

= \frac{1}{3} \cdot \int \frac{arcsin ( u )}{1 - u ^{2}} d u

使用换元积分法

= \frac{1}{3} \cdot \int v d v

使用幂法则

= \frac{1}{3} \cdot \frac{v ^{2}}{2}

代回

= \frac{1}{3} \cdot \frac{arcsin ^{2} ( 3 x )}{2}

化简

\frac{1}{3} \cdot \frac{arcsin ^{2} ( 3 x )}{2} : \frac{1}{6} arcsin^{2} (3 x)

= \frac{1}{6} arcsin^{2} (3 x)

解答补常数

= \frac{1}{6} arcsin^{2} (3 x) + C

作图

流行的例子

derivative y=((x-1))/(x+1)

d er i v a t i v e y = \frac{( x - 1 )}{x + 1}

integral of xysin(x^2y)

\int x y sin (x^{2} y) d x

(\partial)/(\partial y)(2y^3)

\frac{\partial}{\partial y} (2 y^{3})

integral of (16x^2)/((x-24)(x+8)^2)

\int \frac{16 x ^{2}}{( x - 24 ) ( x + 8 ) ^{2}} d x

(\partial)/(\partial y)((x+1)/(y-1))

\frac{\partial}{\partial y} (\frac{x + 1}{y - 1})