integral of (4x^5+10x^3)/(x^2)

解答

\int \frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} d x

x^{4} + 5 x^{2} + C

求解步骤

\int \frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} d x

乘开

\frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} : \frac{4 x ^{5}}{x ^{2}} + \frac{10 x ^{3}}{x ^{2}}

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 \frac{4 x ^{5}}{x ^{2}} d x + \int \frac{10 x ^{3}}{x ^{2}} d x

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

\int \frac{10 x ^{3}}{x ^{2}} d x = 5 x^{2}

= x^{4} + 5 x^{2}

解答补常数

= x^{4} + 5 x^{2} + C

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

\frac{d y}{d x} = 0.72 - \frac{9 y}{1000}, y (0) = 80

\int_{- 1}^{1} x (x^{2} + 9)^{3} d x

d er i v a t i v e 3 3 + tan (t)

y \frac{d y}{d x} + 8 x^{3} = 4