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Beliebt Rechnen >

integral of 8xsec^2(x)

Lösung

\int 8 x sec^{2} (x) d x

Lösung

8 (x tan (x) + ln ∣ cos (x) ∣) + C

Schritte zur Lösung

\int 8 x sec^{2} (x) d x

Entferne die Konstante:

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

= 8 \cdot \int x sec^{2} (x) d x

Wende die partielle Integration an

= 8 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 8 (x tan (x) - (- ln ∣ cos (x) ∣))

Vereinfache

= 8 (x tan (x) + ln ∣ cos (x) ∣)

Füge eine Konstante zur Lösung hinzu

= 8 (x tan (x) + ln ∣ cos (x) ∣) + C

Graph

Beliebte Beispiele

integral of xsin(2ax)

\int x sin (2 a x) d x

derivative y=(1+6x^2)(x-x^2)

d er i v a t i v e y = (1 + 6 x^{2}) (x - x^{2})

sum from n=1 to infinity of 5/(n^4)

n = 1 \sum \infty \frac{5}{n ^{4}}

limit as x approaches infinity of x/(3x)

x \to \infty lim (\frac{x}{3 x})

(d^2)/(dx^2)(1/(4x^2+5x))

\frac{d ^{2}}{d x ^{2}} (\frac{1}{4 x ^{2} + 5 x})