integral of 1/(2sqrt(1-x^2))-3/(1+x^2)

解

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

\frac{1}{2} arcsin (x) - 3 arctan (x) + C

解答ステップ

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

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

\int \frac{3}{1 + x ^{2}} d x = 3 arctan (x)

= \frac{1}{2} arcsin (x) - 3 arctan (x)

定数を解答に追加する

= \frac{1}{2} arcsin (x) - 3 arctan (x) + C