integral of x^{4/3}-3x^{5/2}

解答

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

\frac{3}{7} x^{\frac{7}{3}} - \frac{6}{7} x^{\frac{7}{2}} + C

求解步骤

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

\int x^{\frac{4}{3}} d x = \frac{3}{7} x^{\frac{7}{3}}

\int 3 x^{\frac{5}{2}} d x = \frac{6}{7} x^{\frac{7}{2}}

= \frac{3}{7} x^{\frac{7}{3}} - \frac{6}{7} x^{\frac{7}{2}}

解答补常数

= \frac{3}{7} x^{\frac{7}{3}} - \frac{6}{7} x^{\frac{7}{2}} + C

\int \frac{x ^{3}}{x + 1} d x

\int_{0}^{2} 4 - x^{2} d x

\frac{d}{d t} (1 + 2 t)

\frac{d}{d x} (x^{5} - 4 x^{3} + 2 x - 3)

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