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受欢迎的微积分 >

integral of (2y)/(sqrt(1-4y^2))

解答

\int \frac{2 y}{1 - 4 y ^{2}} d y

解答

- \frac{1}{2} 1 - 4 y^{2} + C

求解步骤

\int \frac{2 y}{1 - 4 y ^{2}} d y

提出常数:

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

= 2 \cdot \int \frac{y}{1 - 4 y ^{2}} d y

使用换元积分法

= 2 \cdot \int - \frac{1}{8 u} d u

提出常数:

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

= 2 (- \frac{1}{8} \cdot \int \frac{1}{u} d u)

使用幂法则

= 2 (- \frac{1}{8} \cdot 2 u^{\frac{1}{2}})

u = 1 - 4 y^{2}

代回

= 2 (- \frac{1}{8} \cdot 2 (1 - 4 y^{2})^{\frac{1}{2}})

化简

2 (- \frac{1}{8} \cdot 2 (1 - 4 y^{2})^{\frac{1}{2}}) : - \frac{1}{2} 1 - 4 y^{2}

= - \frac{1}{2} 1 - 4 y^{2}

解答补常数

= - \frac{1}{2} 1 - 4 y^{2} + C

作图

流行的例子

integral of sqrt(144-36x^2)

\int 144 - 36 x^{2} d x

integral of 1/(sin^2(x/2))

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

integral of 5/(x^2)sin^2(-5/x)

\int \frac{5}{x ^{2}} sin^{2} (- \frac{5}{x}) d x

integral of (3x-5)/(x^2+5)

\int \frac{3 x - 5}{x ^{2} + 5} d x

integral of 1/(x^{1.04)}

\int \frac{1}{x ^{1.04}} d x