integral of x^3+x^2

解答

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

\frac{x ^{4}}{4} + \frac{x ^{3}}{3} + C

求解步骤

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3}

解答补常数

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + C

\frac{d}{d x} (4 - x^{2} + y^{2})

\int (\frac{12 x ^{4} + 3 x ^{2} + 6 a x}{2 x}) d x

x \to 3 + lim (\frac{7}{x - 3})

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

n = 0 \sum \infty \frac{1}{( 2 ^{n} )}