受欢迎的 >

integral of (3x^2+9x^4-x)/(x^2)

解答

\int \frac{3 x ^{2} + 9 x ^{4} - x}{x ^{2}} d x

3 x + 3 x^{3} - ln ∣ x ∣ + C

求解步骤

\int \frac{3 x ^{2} + 9 x ^{4} - x}{x ^{2}} d x

乘开

\frac{3 x ^{2} + 9 x ^{4} - x}{x ^{2}} : 3 + 9 x^{2} - \frac{1}{x}

= \int 3 + 9 x^{2} - \frac{1}{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 3 d x + \int 9 x^{2} d x - \int \frac{1}{x} d x

\int 3 d x = 3 x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 3 x + 3 x^{3} - ln ∣ x ∣

解答补常数

= 3 x + 3 x^{3} - ln ∣ x ∣ + C

\int \frac{x + 5}{x ^{2} - 2 x - 8} d x

\int (x + 4 x - 5) d x

\int tanh (\frac{x}{7}) d x

\int \frac{8 x ^{2} + 5 x + 8}{x ^{3} - 1} d x

\int (100 + 2 t)^{\frac{3}{2}} d t