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integral of 4/((4x-3)ln(4x-3))

解答

\int \frac{4}{( 4 x - 3 ) ln ( 4 x - 3 )} d x

解答

ln ∣ ln (4 x - 3) ∣ + C

求解步骤

\int \frac{4}{( 4 x - 3 ) ln ( 4 x - 3 )} d x

提出常数:

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

= 4 \cdot \int \frac{1}{( 4 x - 3 ) ln ( 4 x - 3 )} d x

使用换元积分法

: \int \frac{1}{4 u ln ( u )} d u

= 4 \cdot \int \frac{1}{4 u ln ( u )} d u

提出常数:

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

= 4 \cdot \frac{1}{4} \cdot \int \frac{1}{u ln ( u )} d u

使用换元积分法

: \int \frac{1}{v} d v

= 4 \cdot \frac{1}{4} \cdot \int \frac{1}{v} d v

使用积分常见定则:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 4 \cdot \frac{1}{4} ln ∣ v ∣

代回

= 4 \cdot \frac{1}{4} ln ∣ ln (4 x - 3) ∣

化简

4 \cdot \frac{1}{4} ln ∣ ln (4 x - 3) ∣ : ln ∣ ln (4 x - 3) ∣

= ln ∣ ln (4 x - 3) ∣

解答补常数

= ln ∣ ln (4 x - 3) ∣ + C

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