integral of (x+1)ln(2x+4)

解答

\int (x + 1) ln (2 x + 4) d x

ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4} + C

求解步骤

\int (x + 1) ln (2 x + 4) d x

使用分布积分法

= ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \int \frac{x}{2} d x

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4}

解答补常数

= ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4} + C

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) (x + 7 x^{3}))

\frac{d y}{d x} = x (9 - y)

\frac{d}{d x} (\frac{1 + 3 x}{1 - 3 x})

x \to \infty lim (9)

d er i v a t i v e - 3 cos (x) + 2 sin (x)