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人気のある微分積分 >

integral of sec^3(1-4x)

解

\int sec^{3} (1 - 4 x) d x

解

- \frac{1}{4} (\frac{sec ^{2} ( 1 - 4 x ) sin ( 1 - 4 x )}{2} + \frac{1}{2} ln ∣ tan (1 - 4 x) + sec (1 - 4 x) ∣) + C

解答ステップ

\int sec^{3} (1 - 4 x) d x

u置換積分法を適用する

= \int - \frac{1}{4} sec^{3} (u) d u

定数を除く:

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

= - \frac{1}{4} \cdot \int sec^{3} (u) d u

積分換算を適用する

= - \frac{1}{4} (\frac{sec ^{2} ( u ) sin ( u )}{2} + \frac{1}{2} \cdot \int sec (u) d u)

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

= - \frac{1}{4} (\frac{sec ^{2} ( u ) sin ( u )}{2} + \frac{1}{2} ln ∣ tan (u) + sec (u) ∣)

代用を戻す

u = 1 - 4 x

= - \frac{1}{4} (\frac{sec ^{2} ( 1 - 4 x ) sin ( 1 - 4 x )}{2} + \frac{1}{2} ln ∣ tan (1 - 4 x) + sec (1 - 4 x) ∣)

定数を解答に追加する

= - \frac{1}{4} (\frac{sec ^{2} ( 1 - 4 x ) sin ( 1 - 4 x )}{2} + \frac{1}{2} ln ∣ tan (1 - 4 x) + sec (1 - 4 x) ∣) + C

グラフ

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