integral of (5x^3-3sqrt(x))/x

解答

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

\frac{5 x ^{3}}{3} - 6 x + C

求解步骤

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

乘开

\frac{5 x ^{3} - 3 x}{x} : 5 x^{2} - \frac{3}{x}

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

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

\int \frac{3}{x} d x = 6 x

= \frac{5 x ^{3}}{3} - 6 x

解答补常数

= \frac{5 x ^{3}}{3} - 6 x + C

\int_{22}^{4} \frac{1}{t ^{3} t ^{2} - 4} d t

y^{^{'}} + y cos (x) = 0

t a y l or x + 1

\int_{1}^{2} \frac{x ^{2} + 8}{3 x - x ^{2}} d x

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