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受欢迎的微积分 >

integral of (5.45)/((1+1.9x)^{0.9)}

解答

\int \frac{5.45}{( 1 + 1.9 x ) ^{0.9}} d x

解答

28.68421 \dots (1 + 1.9 x)^{0.1} + C

求解步骤

\int \frac{5.45}{( 1 + 1.9 x ) ^{0.9}} d x

提出常数:

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

= 5.45 \cdot \int \frac{1}{( 1 + 1.9 x ) ^{0.9}} d x

使用换元积分法

= 5.45 \cdot \int \frac{1}{1.9 u ^{0.9}} d u

提出常数:

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

= 5.45 \cdot \frac{1}{1.9} \cdot \int \frac{1}{u ^{0.9}} d u

化简

= 5.45 \cdot 0.52631 \dots \cdot \int \frac{1}{u ^{0.9}} d u

使用幂法则

= 5.45 \cdot 0.52631 \dots \cdot 10 u^{0.1}

u = 1 + 1.9 x

代回

= 5.45 \cdot 0.52631 \dots \cdot 10 (1 + 1.9 x)^{0.1}

化简

= 28.68421 \dots (1 + 1.9 x)^{0.1}

解答补常数

= 28.68421 \dots (1 + 1.9 x)^{0.1} + C

作图

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