integral of {y(2ax+by)}

解答

\int {y (2 a x + b y)} d x

y (b y x + a x^{2}) + C

求解步骤

\int y (2 a x + b y) d x

提出常数:

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

= y \cdot \int b y + 2 a x d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= y (\int b y d x + \int 2 a x d x)

\int b y d x = b y x

\int 2 a x d x = a x^{2}

= y (b y x + a x^{2})

解答补常数

= y (b y x + a x^{2}) + C

x \to - 3 lim (\frac{2}{x + 3})

\frac{d}{d x} (\frac{x ^{2} - 2 x + 5}{x ^{2} + 2 x - 3})

\int \frac{4 x ^{5} - 4}{x ^{2} - 4} d x

n = 1 \sum \infty \frac{n}{1 + n ^{2}}

\frac{\partial}{\partial y} (ln (e^{x} + e^{y}))