integral of-x^{-3/2}

解答

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

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

求解步骤

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

提出常数:

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

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

使用幂法则

: - \frac{2}{x ^{\frac{1}{2}}}

= - (- \frac{2}{x ^{\frac{1}{2}}})

化简

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

解答补常数

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

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

\int 9 x (\frac{1}{x} + x^{2}) d x

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

\int sec^{2} (2 x) cos^{2} (2 x) d x

\int \frac{25 - 9 x ^{2}}{x ^{2}} d x