integral of xsin(1/5)x

解答

\int x sin (\frac{1}{5}) x d x

\frac{1}{3} sin (\frac{1}{5}) x^{3} + C

求解步骤

\int x sin (\frac{1}{5}) x d x

提出常数:

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

= sin (\frac{1}{5}) \cdot \int xx d x

化简

xx : x^{2}

= sin (\frac{1}{5}) \cdot \int x^{2} d x

使用幂法则

= sin (\frac{1}{5}) \frac{x ^{3}}{3}

化简

sin (\frac{1}{5}) \frac{x ^{3}}{3} : \frac{1}{3} sin (\frac{1}{5}) x^{3}

= \frac{1}{3} sin (\frac{1}{5}) x^{3}

解答补常数

= \frac{1}{3} sin (\frac{1}{5}) x^{3} + C

x \to 7.7 lim (8.9 x + 8.8)

\frac{\partial}{\partial x} (3 x sin (x y))

\int x^{2} + c d x

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

d er i v a t i v e f (x) = x^{2} (x^{3} - 1)