integral from 1 to 6x of 7/t

解答

\int_{1}^{6 x} \frac{7}{t} d t

7 ln (6 ∣ x ∣)

求解步骤

\int_{1}^{6 x} \frac{7}{t} d t

提出常数:

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

= 7 \cdot \int_{1}^{6 x} \frac{1}{t} d t

使用积分常见定则:

\int \frac{1}{t} d t = ln (∣ t ∣)

= 7 [ln ∣ t ∣]_{1}^{6 x}

带入上下限计算后得:

ln (6 ∣ x ∣)

= 7 ln (6 ∣ x ∣)

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