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受欢迎的微积分 >

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

解答

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

解答

- - x^{2} + 1 + C

求解步骤

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

使用换元积分法

= \int - \frac{1}{2 u} d u

提出常数:

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

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

使用幂法则

= - \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

u = - x^{2} + 1

代回

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

化简

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

= - - x^{2} + 1

解答补常数

= - - x^{2} + 1 + C

作图

流行的例子

integral of 1/((sin(x)+1))

\int \frac{1}{( sin ( x ) + 1 )} d x

integral of (4x+3x^2-2/(x^2))

\int (4 x + 3 x^{2} - \frac{2}{x ^{2}}) d x

integral of (2x+4)/(x^2+4x+1)

\int \frac{2 x + 4}{x ^{2} + 4 x + 1} d x

积分 2cos^2(x)

in t e g r a l 2 cos^{2} (x)

integral of 1/x*(x^5)/5

\int \frac{1}{x} \cdot \frac{x ^{5}}{5} d x