integral of 4ln(\sqrt[3]{x})

解答

\int 4 ln (3 x) d x

4 (\frac{1}{3} x ln (x) - \frac{1}{3} x) + C

求解步骤

\int 4 ln (3 x) d x

提出常数:

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

= 4 \cdot \int ln (3 x) d x

使用分布积分法

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

\int \frac{1}{3} d x = \frac{1}{3} x

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

化简

ln (3 x) : \frac{1}{3} ln (x)

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

解答补常数

= 4 (\frac{1}{3} x ln (x) - \frac{1}{3} x) + C

\int \frac{9 e ^{- \frac{1}{x}}}{x ^{2}} d x

t an g e n t f (x) = x^{2} + 1, at x = 2

t an g e n t x^{4} - 4 x^{2} + 10, at x = 1

y^{^{'}} + x y = 0

x \to 0 + lim (cot^{2} (x))