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人気のある微分積分 >

integral of (sec(7x))/7

解

\int \frac{sec ( 7 x )}{7} d x

解

\frac{1}{49} ln ∣ tan (7 x) + sec (7 x) ∣ + C

解答ステップ

\int \frac{sec ( 7 x )}{7} d x

定数を除く:

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

= \frac{1}{7} \cdot \int sec (7 x) d x

u置換積分法を適用する

= \frac{1}{7} \cdot \int sec (u) \frac{1}{7} d u

定数を除く:

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

= \frac{1}{7} \cdot \frac{1}{7} \cdot \int sec (u) d u

共通積分を使用する:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= \frac{1}{7} \cdot \frac{1}{7} ln ∣ tan (u) + sec (u) ∣

代用を戻す

u = 7 x

= \frac{1}{7} \cdot \frac{1}{7} ln ∣ tan (7 x) + sec (7 x) ∣

簡素化

\frac{1}{7} \cdot \frac{1}{7} ln ∣ tan (7 x) + sec (7 x) ∣ : \frac{1}{49} ln ∣ tan (7 x) + sec (7 x) ∣

= \frac{1}{49} ln ∣ tan (7 x) + sec (7 x) ∣

定数を解答に追加する

= \frac{1}{49} ln ∣ tan (7 x) + sec (7 x) ∣ + C

グラフ

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