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Beliebt Rechnen >

integral of sec^3(1-4x)

Lösung

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

Lösung

- \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

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende integrale Reduktion an

= - \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) ∣)

Setze in

u = 1 - 4 x

ein

= - \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) ∣)

Füge eine Konstante zur Lösung hinzu

= - \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

Graph

Beliebte Beispiele

y^{''}-10y^'+25y=0,y(0)=0,y^'(0)=3

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 3

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