integral of 2x^3-2/3 x^2+5x

解答

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

\frac{x ^{4}}{2} - \frac{2 x ^{3}}{9} + \frac{5 x ^{2}}{2} + C

求解步骤

\int 2 x^{3} - \frac{2}{3} x^{2} + 5 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

= \int 2 x^{3} d x - \int \frac{2}{3} x^{2} d x + \int 5 x d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int \frac{2}{3} x^{2} d x = \frac{2 x ^{3}}{9}

\int 5 x d x = \frac{5 x ^{2}}{2}

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{9} + \frac{5 x ^{2}}{2}

解答补常数

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{9} + \frac{5 x ^{2}}{2} + C

x \to 0 lim (\frac{sin ( 10 x )}{x})

\int_{0}^{2} \frac{4 x + 3}{x ^{4}} d x

\int (5 x^{3} - 7 x^{2} + 2 x + 1) d x

\frac{d}{d x} (30 + \frac{1}{x + 1} - 3 x^{2})

\frac{d}{d x} (\frac{1}{5 x ^{2} + 2 x})