integral of 5/(sqrt(1-9x^2))+7x

解

\int \frac{5}{1 - 9 x ^{2}} + 7 x d x

\frac{5}{3} arcsin (3 x) + \frac{7 x ^{2}}{2} + C

解答ステップ

\int \frac{5}{1 - 9 x ^{2}} + 7 x 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{5}{1 - 9 x ^{2}} d x + \int 7 x d x

\int \frac{5}{1 - 9 x ^{2}} d x = \frac{5}{3} arcsin (3 x)

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

= \frac{5}{3} arcsin (3 x) + \frac{7 x ^{2}}{2}

定数を解答に追加する

= \frac{5}{3} arcsin (3 x) + \frac{7 x ^{2}}{2} + C