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受欢迎的微积分 >

integral of (17.6x)/(sqrt(17.6x^2+1))

解答

\int \frac{17.6 x}{17.6 x ^{2} + 1} d x

解答

1 17.6 x^{2} + 1 + C

求解步骤

\int \frac{17.6 x}{17.6 x ^{2} + 1} d x

提出常数:

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

= 17.6 \cdot \int \frac{x}{17.6 x ^{2} + 1} d x

使用换元积分法

= 17.6 \cdot \int \frac{1}{35.2 u} d u

提出常数:

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

= 17.6 \cdot \frac{1}{35.2} \cdot \int \frac{1}{u} d u

化简

= 17.6 \cdot 0.02840 \dots \cdot \int \frac{1}{u} d u

使用幂法则

= 17.6 \cdot 0.02840 \dots \cdot 2 u^{\frac{1}{2}}

u = 17.6 x^{2} + 1

代回

= 17.6 \cdot 0.02840 \dots \cdot 2 (17.6 x^{2} + 1)^{\frac{1}{2}}

化简

17.6 \cdot 0.02840 \dots \cdot 2 (17.6 x^{2} + 1)^{\frac{1}{2}} : 1 17.6 x^{2} + 1

= 1 17.6 x^{2} + 1

解答补常数

= 1 17.6 x^{2} + 1 + C

作图

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