integral of x^2+2x-3

解答

\int x^{2} + 2 x - 3 d x

\frac{x ^{3}}{3} + x^{2} - 3 x + C

求解步骤

\int x^{2} + 2 x - 3 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

= \int x^{2} d x + \int 2 x d x - \int 3 d x

\int x^{2} d x = \frac{x ^{3}}{3}

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

\int 3 d x = 3 x

= \frac{x ^{3}}{3} + x^{2} - 3 x

解答补常数

= \frac{x ^{3}}{3} + x^{2} - 3 x + C

\int (x^{2} + 4) d x

θ \to 0 lim (\frac{sin ( θ )}{sin ( 2 θ )})

\frac{\partial}{\partial x} (5 x cos (x) cos (y))

n = 1 \sum \infty 0. 7^{n}

d er i v a t i v e e^{\frac{z}{z - 1}}