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Beliebt Rechnen >

integral of sec^2(xta)n^5x

Lösung

\int sec^{2} (x t a) n^{5} x d x

Lösung

n^{5} \frac{1}{a ^{2} t ^{2}} (a t x tan (a t x) + ln ∣ cos (a t x) ∣) + C

Schritte zur Lösung

\int sec^{2} (x t a) n^{5} x d x

Entferne die Konstante:

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

= n^{5} \cdot \int sec^{2} (a t x) x d x

Wende U-Substitution an

= n^{5} \cdot \int \frac{u sec ^{2} ( u )}{a ^{2} t ^{2}} d u

Entferne die Konstante:

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

= n^{5} \frac{1}{a ^{2} t ^{2}} \cdot \int u sec^{2} (u) d u

Wende die partielle Integration an

= n^{5} \frac{1}{a ^{2} t ^{2}} (u tan (u) - \int tan (u) d u)

\int tan (u) d u = - ln ∣ cos (u) ∣

= n^{5} \frac{1}{a ^{2} t ^{2}} (u tan (u) - (- ln ∣ cos (u) ∣))

Setze in

u = a t x

ein

= n^{5} \frac{1}{a ^{2} t ^{2}} (a t x tan (a t x) - (- ln ∣ cos (a t x) ∣))

Vereinfache

= n^{5} \frac{1}{a ^{2} t ^{2}} (a t x tan (a t x) + ln ∣ cos (a t x) ∣)

Füge eine Konstante zur Lösung hinzu

= n^{5} \frac{1}{a ^{2} t ^{2}} (a t x tan (a t x) + ln ∣ cos (a t x) ∣) + C

Graph

Beliebte Beispiele

derivative (1/(y^2)-5/(y^4))(y+3y^3)

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 3 y^{3})

limit as x approaches 3+of 18ln(x-3)

x \to 3 + lim (18 ln (x - 3))

derivative of e^5

\frac{d}{d x} (e^{5})

integral of (tan(x))/x

\int \frac{tan ( x )}{x} d x

laplacetransform e^{-t}t^2

l a pl a ce t r an s f or m e^{- t} t^{2}