integral of xsec(4x^2-5)

Lösung

\int x sec (4 x^{2} - 5) d x

\frac{1}{8} ln tan (4 x^{2} - 5) + sec (4 x^{2} - 5) + C

Schritte zur Lösung

\int x sec (4 x^{2} - 5) d x

Wende U-Substitution an

= \int \frac{sec ( u )}{8} d u

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int sec (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{8} ln ∣ tan (u) + sec (u) ∣

Setze in

u = 4 x^{2} - 5

ein

= \frac{1}{8} ln tan (4 x^{2} - 5) + sec (4 x^{2} - 5)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{8} ln tan (4 x^{2} - 5) + sec (4 x^{2} - 5) + C

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