integral of 2/3 t^{3/2}-2sin(t)+C

解答

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

\frac{4}{15} t^{\frac{5}{2}} + 2 cos (t) + Ct + C

求解步骤

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

\int \frac{2}{3} t^{\frac{3}{2}} d t = \frac{4}{15} t^{\frac{5}{2}}

\int 2 sin (t) d t = - 2 cos (t)

\int C d t = Ct

= \frac{4}{15} t^{\frac{5}{2}} - (- 2 cos (t)) + Ct

化简

= \frac{4}{15} t^{\frac{5}{2}} + 2 cos (t) + Ct

解答补常数

= \frac{4}{15} t^{\frac{5}{2}} + 2 cos (t) + Ct + C

\int (5 x - x^{2}) d x

\int \frac{x}{3 x} d x

\int 10 x^{5} e^{x} d x

7 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

f^{'} (t)