integral of 4/15 t^{5/2}+2cos(t)+Ct+C

解答

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

\frac{8}{105} t^{\frac{7}{2}} + 2 sin (t) + \frac{C t ^{2}}{2} + Ct + C

求解步骤

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

\int \frac{4}{15} t^{\frac{5}{2}} d t = \frac{8}{105} t^{\frac{7}{2}}

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

\int Ct d t = \frac{C t ^{2}}{2}

\int C d t = Ct

= \frac{8}{105} t^{\frac{7}{2}} + 2 sin (t) + \frac{C t ^{2}}{2} + Ct

解答补常数

= \frac{8}{105} t^{\frac{7}{2}} + 2 sin (t) + \frac{C t ^{2}}{2} + Ct + C

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