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受欢迎的微积分 >

integral of (5.4145)/(sqrt(1+0.91x))

解答

\int \frac{5.4145}{1 + 0.91 x} d x

解答

11.9 1 + 0.91 x + C

求解步骤

\int \frac{5.4145}{1 + 0.91 x} d x

提出常数:

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

= 5.4145 \cdot \int \frac{1}{1 + 0.91 x} d x

使用换元积分法

= 5.4145 \cdot \int \frac{1}{0.91 u} d u

提出常数:

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

= 5.4145 \cdot \frac{1}{0.91} \cdot \int \frac{1}{u} d u

化简

= 5.4145 \cdot 1.09890 \dots \cdot \int \frac{1}{u} d u

使用幂法则

= 5.4145 \cdot 1.09890 \dots \cdot 2 u^{\frac{1}{2}}

u = 1 + 0.91 x

代回

= 5.4145 \cdot 1.09890 \dots \cdot 2 (1 + 0.91 x)^{\frac{1}{2}}

化简

5.4145 \cdot 1.09890 \dots \cdot 2 (1 + 0.91 x)^{\frac{1}{2}} : 11.9 1 + 0.91 x

= 11.9 1 + 0.91 x

解答补常数

= 11.9 1 + 0.91 x + C

作图

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