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受欢迎的微积分 >

integral of (2t)/(sqrt(25-t^2))

解答

\int \frac{2 t}{25 - t ^{2}} d t

解答

- 2 25 - t^{2} + C

求解步骤

\int \frac{2 t}{25 - t ^{2}} d t

提出常数:

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

= 2 \cdot \int \frac{t}{25 - t ^{2}} d t

使用换元积分法

= 2 \cdot \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

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

使用幂法则

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

u = 25 - t^{2}

代回

= 2 (- \frac{1}{2} \cdot 2 (25 - t^{2})^{\frac{1}{2}})

化简

2 (- \frac{1}{2} \cdot 2 (25 - t^{2})^{\frac{1}{2}}) : - 2 25 - t^{2}

= - 2 25 - t^{2}

解答补常数

= - 2 25 - t^{2} + C

作图

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