integral of 2sqrt(x)-\sqrt[3]{x}-x^4

解答

\int 2 x - 3 x - x^{4} d x

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

求解步骤

\int 2 x - 3 x - x^{4} 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 d x - \int 3 x d x - \int x^{4} d x

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

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

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

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

解答补常数

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

\frac{\partial}{\partial x} (- \frac{x}{x ^{2} + y ^{2}})

\int 5 cos (x) - 4 sin (x) d x

d er i v a t i v e y = 4 (cos (x))^{3}

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

d er i v a t i v e f (x) = a^{4} + cos^{4} (x)