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人気のある微分積分 >

integral of 1/(1-sec(x))

解

\int \frac{1}{1 - sec ( x )} d x

解

cot (\frac{x}{2}) + x + C

解答ステップ

\int \frac{1}{1 - sec ( x )} d x

因数

1 - sec (x) : - (- 1 + sec (x))

= \int \frac{1}{- ( - 1 + sec ( x ) )} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{- 1 + sec ( x )} d x

\frac{1}{- 1 + sec ( x )} = \frac{sec ( x )}{- 1 + sec ( x )} - 1

= - \int \frac{sec ( x )}{- 1 + sec ( x )} - 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 \frac{sec ( x )}{- 1 + sec ( x )} d x - \int 1 d x)

\int \frac{sec ( x )}{- 1 + sec ( x )} d x = - cot (\frac{x}{2})

\int 1 d x = x

= - (- cot (\frac{x}{2}) - x)

簡素化

= cot (\frac{x}{2}) + x

定数を解答に追加する

= cot (\frac{x}{2}) + x + C

グラフ

人気の例

integral of cos((npix)/5)

\int cos (\frac{nπ x}{5}) d x

integral of 3/(x^3-1)

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

integral of sin^3(9x)cos(9x)

\int sin^{3} (9 x) cos (9 x) d x

integral of sqrt(R^2-x^2)

\int R^{2} - x^{2} d x

integral of (x^2)/(x^2-16)

\int \frac{x ^{2}}{x ^{2} - 16} d x