integral of (3x^2-2/(x^3)+\sqrt[3]{x}-8)

解答

\int (3 x^{2} - \frac{2}{x ^{3}} + 3 x - 8) d x

x^{3} + \frac{1}{x ^{2}} + \frac{3}{4} x^{\frac{4}{3}} - 8 x + C

求解步骤

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

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

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

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

\int 8 d x = 8 x

= x^{3} - (- \frac{1}{x ^{2}}) + \frac{3}{4} x^{\frac{4}{3}} - 8 x

化简

= x^{3} + \frac{1}{x ^{2}} + \frac{3}{4} x^{\frac{4}{3}} - 8 x

解答补常数

= x^{3} + \frac{1}{x ^{2}} + \frac{3}{4} x^{\frac{4}{3}} - 8 x + C

d er i v a t i v e \frac{2 x}{x ^{2} + 1}

x^{^{''}} + 3 x^{^{'}} + 2 x = e^{- t}

t an g e n t (3 x + 25)

\frac{\partial}{\partial x} (e^{2 x} cos (y))

x \to - 2 lim (3 x + 4)