integral of (7x^2)ex^3+1

解

\int (7 x^{2}) e x^{3} + 1 d x

\frac{7 e x ^{6}}{6} + x + C

解答ステップ

\int 7 x^{2} e x^{3} + 1 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 7 x^{2} e x^{3} d x + \int 1 d x

\int 7 x^{2} e x^{3} d x = \frac{7 e x ^{6}}{6}

\int 1 d x = x

= \frac{7 e x ^{6}}{6} + x

定数を解答に追加する

= \frac{7 e x ^{6}}{6} + x + C