integral of (xsqrt(x))/2

解答

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

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

求解步骤

\int \frac{x x}{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 x d x

化简

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

= \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

d er i v a t i v e f (x) = \frac{( 4 x + x ^{2} )}{( 2 + x ) ^{2}}

\int \frac{14 - 14 x}{1 - x} d x

\frac{d y}{d t} = - \frac{t}{e ^{y + t^{2}}}

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

\frac{d}{d x} (arccosh (x))