integral of 7x^2+3+6/(x^2+1)

解

\int 7 x^{2} + 3 + \frac{6}{x ^{2} + 1} d x

\frac{7 x ^{3}}{3} + 3 x + 6 arctan (x) + C

解答ステップ

\int 7 x^{2} + 3 + \frac{6}{x ^{2} + 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} d x + \int 3 d x + \int \frac{6}{x ^{2} + 1} d x

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

\int 3 d x = 3 x

\int \frac{6}{x ^{2} + 1} d x = 6 arctan (x)

= \frac{7 x ^{3}}{3} + 3 x + 6 arctan (x)

定数を解答に追加する

= \frac{7 x ^{3}}{3} + 3 x + 6 arctan (x) + C