integral of 1/5 x

解答

\int \frac{1}{5} x d x

\frac{x ^{2}}{10} + C

求解步骤

\int \frac{1}{5} x d x

提出常数:

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

= \frac{1}{5} \cdot \int x d x

使用幂法则

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

化简

\frac{1}{5} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{10}

= \frac{x ^{2}}{10}

解答补常数

= \frac{x ^{2}}{10} + C

\int \frac{2}{x ^{3} x ^{4} - 81} d x

\frac{d}{d t} (e^{- a t} cos (wt))

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

\frac{d}{d x} (\frac{( 3 x ^{2} + 1 ) ^{3}}{( 2 x ^{2} - 1 ) ^{4}})

f^{^{'}} (x) = a^{2 x}