integral of (x^{3/2})/2

解答

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

\frac{1}{5} x^{\frac{5}{2}} + C

求解步骤

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

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

使用幂法则

= \frac{1}{2} \cdot \frac{2}{5} x^{\frac{5}{2}}

化简

\frac{1}{2} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{1}{5} x^{\frac{5}{2}}

= \frac{1}{5} x^{\frac{5}{2}}

解答补常数

= \frac{1}{5} x^{\frac{5}{2}} + C

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

\int \frac{2}{2 u + 1 - u ^{2}} d u

\int \frac{1}{12 x - 2} d x

\int (x + 1) cos (n x) d x

\int (3 x^{5} - 5 x^{2} - 3 x) d x