integral of tan^2(w/2)+sec^2(w/2)

解

\int tan^{2} (\frac{w}{2}) + sec^{2} (\frac{w}{2}) d w

- w + 4 tan (\frac{w}{2}) + C

解答ステップ

\int tan^{2} (\frac{w}{2}) + sec^{2} (\frac{w}{2}) d w

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 tan^{2} (\frac{w}{2}) d w + \int sec^{2} (\frac{w}{2}) d w

\int tan^{2} (\frac{w}{2}) d w = - w + 2 tan (\frac{w}{2})

\int sec^{2} (\frac{w}{2}) d w = 2 tan (\frac{w}{2})

= - w + 2 tan (\frac{w}{2}) + 2 tan (\frac{w}{2})

簡素化

= - w + 4 tan (\frac{w}{2})

定数を解答に追加する

= - w + 4 tan (\frac{w}{2}) + C