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

解

\int sec (x) tan (x) + \frac{1}{1 - x ^{2}} d x

sec (x) + arcsin (x) + C

解答ステップ

\int sec (x) tan (x) + \frac{1}{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 sec (x) tan (x) d x + \int \frac{1}{1 - x ^{2}} d x

\int sec (x) tan (x) d x = sec (x)

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

= sec (x) + arcsin (x)

定数を解答に追加する

= sec (x) + arcsin (x) + C