integral of 8sin(2)(x)cos(3)(x)

解答

\int 8 sin (2) (x) cos (3) (x) d x

\frac{8}{3} sin (2) cos (3) x^{3} + C

求解步骤

\int 8 sin (2) x cos (3) x d x

提出常数:

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

= 8 sin (2) cos (3) \cdot \int xx d x

化简

xx : x^{2}

= 8 sin (2) cos (3) \cdot \int x^{2} d x

使用幂法则

= 8 sin (2) cos (3) \frac{x ^{3}}{3}

化简

8 sin (2) cos (3) \frac{x ^{3}}{3} : \frac{8}{3} sin (2) cos (3) x^{3}

= \frac{8}{3} sin (2) cos (3) x^{3}

解答补常数

= \frac{8}{3} sin (2) cos (3) x^{3} + C

x \to 0 lim (\frac{1 - cos ( 2 x )}{x})

x \to 1 + lim (\frac{1}{x - 1} - \frac{1}{ln ( x )})

\int \frac{( e ^{6 x} )}{e ^{6 x} + 1} d x

\frac{d y}{d t} = (t y)^{2}

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