integral of sqrt(t)-5cos(t)

解答

\int t - 5 cos (t) d t

\frac{2}{3} t^{\frac{3}{2}} - 5 sin (t) + C

求解步骤

\int t - 5 cos (t) d t

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t d t - \int 5 cos (t) d t

\int t d t = \frac{2}{3} t^{\frac{3}{2}}

\int 5 cos (t) d t = 5 sin (t)

= \frac{2}{3} t^{\frac{3}{2}} - 5 sin (t)

解答补常数

= \frac{2}{3} t^{\frac{3}{2}} - 5 sin (t) + C

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

\frac{d y}{d x} = 14 x^{8}

\frac{d}{d x} (x \cdot ∣ x ∣)

x \to - 1 lim (x + a)

x \to 2 lim (2 e^{x - 2})