integral of 4/15 x^{5/2}+6cos(x)+Cx+D

解

\int \frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x + D d x

\frac{8}{105} x^{\frac{7}{2}} + 6 sin (x) + \frac{C x ^{2}}{2} + D x + C

解答ステップ

\int \frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x + D d x

総和規則を適用する:

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

= \int \frac{4}{15} x^{\frac{5}{2}} d x + \int 6 cos (x) d x + \int C x d x + \int D d x

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

\int 6 cos (x) d x = 6 sin (x)

\int C x d x = \frac{C x ^{2}}{2}

\int D d x = D x

= \frac{8}{105} x^{\frac{7}{2}} + 6 sin (x) + \frac{C x ^{2}}{2} + D x

定数を解答に追加する

= \frac{8}{105} x^{\frac{7}{2}} + 6 sin (x) + \frac{C x ^{2}}{2} + D x + C