integral of sqrt(3x^3)

解答

\int 3 x^{3} d x

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

求解步骤

\int 3 x^{3} d x

使用分布积分法

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

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

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

3 x x x^{2} = 3 x^{2} x

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

解答补常数

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

\int csc^{4} (\frac{x}{4}) d x

\int \frac{sin ( y \cdot x )}{y} d y

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

\int t + 3 d t

\int (2 x^{6} + x^{2} - x - 2) d x