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受欢迎的微积分 >

integral of 2/((1-x^2)^{3/2)}

解答

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

解答

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

求解步骤

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

使用三角换元法

= 2 \cdot \int sec^{2} (u) d u

使用积分常见定则:

\int sec^{2} (u) d u = tan (u)

= 2 tan (u)

u = arcsin (x)

代回

= 2 tan (arcsin (x))

化简

2 tan (arcsin (x)) : \frac{2 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

= \frac{2 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

解答补常数

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

作图

流行的例子

inverselaplace 1/((s*(s+1)))

in v erse l a pl a ce \frac{1}{( s \cdot ( s + 1 ) )}

integral of (x^2)/(16+9x^2)

\int \frac{x ^{2}}{16 + 9 x ^{2}} d x

integral from 1 to 2 of 2x-x^2

\int_{1}^{2} 2 x - x^{2} d x

integral of 1/(x^2-2x+37)

\int \frac{1}{x ^{2} - 2 x + 37} d x

(dx)/(dt)+x^2=x

\frac{d x}{d t} + x^{2} = x