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受欢迎的微积分 >

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

解答

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

解答

ln ∣ ln (3 x + 4) ∣ + C

求解步骤

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

提出常数:

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

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

使用换元积分法

= 3 \cdot \int \frac{1}{3 u ln ( u )} d u

提出常数:

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

= 3 \cdot \frac{1}{3} \cdot \int \frac{1}{u ln ( u )} d u

使用换元积分法

= 3 \cdot \frac{1}{3} \cdot \int \frac{1}{v} d v

使用积分常见定则:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 3 \cdot \frac{1}{3} ln ∣ v ∣

代回

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

化简

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

= ln ∣ ln (3 x + 4) ∣

解答补常数

= ln ∣ ln (3 x + 4) ∣ + C

作图

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