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受欢迎的微积分 >

integral of 7/(4+7x)

解答

\int \frac{7}{4 + 7 x} d x

解答

ln ∣ 4 + 7 x ∣ + C

求解步骤

\int \frac{7}{4 + 7 x} d x

提出常数:

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

= 7 \cdot \int \frac{1}{4 + 7 x} d x

使用换元积分法

= 7 \cdot \int \frac{1}{7 u} d u

提出常数:

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

= 7 \cdot \frac{1}{7} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 7 \cdot \frac{1}{7} ln ∣ u ∣

u = 4 + 7 x

代回

= 7 \cdot \frac{1}{7} ln ∣ 4 + 7 x ∣

化简

7 \cdot \frac{1}{7} ln ∣ 4 + 7 x ∣ : ln ∣ 4 + 7 x ∣

= ln ∣ 4 + 7 x ∣

解答补常数

= ln ∣ 4 + 7 x ∣ + C

作图

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