integral of 9xsqrt(x)

解答

\int 9 x x d x

\frac{18}{5} x^{\frac{5}{2}} + C

求解步骤

\int 9 x x d x

提出常数:

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

= 9 \cdot \int x x d x

化简

x x : x^{\frac{3}{2}}

= 9 \cdot \int x^{\frac{3}{2}} d x

使用幂法则

= 9 \cdot \frac{2}{5} x^{\frac{5}{2}}

化简

9 \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{18}{5} x^{\frac{5}{2}}

= \frac{18}{5} x^{\frac{5}{2}}

解答补常数

= \frac{18}{5} x^{\frac{5}{2}} + C

\int (x sin (1 + x^{\frac{3}{2}})) d x

\int \frac{x ^{2}}{- 16 x ^{2} + 1} d x

\int \frac{7}{16 - 4 t ^{2}} d t

\int 4 x x + 1 d x

\int 8 x e^{7 x^{2}} d x