de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to pi/4 of sec^5(x)

Lösung

\int_{0}^{\frac{π}{4}} sec^{5} (x) d x

Lösung

\frac{3 2 ln ( 1 + 2 ) + 14}{8 2}

+1

Dezimale

1.56795 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} sec^{5} (x) d x

Wende integrale Reduktion an

= [\frac{sec ^{4} ( x ) sin ( x )}{4}]_{0}^{\frac{π}{4}} + \frac{3}{4} \cdot \int_{0}^{\frac{π}{4}} sec^{3} (x) d x

\int_{0}^{\frac{π}{4}} sec^{3} (x) d x = \frac{2 + ln ( 1 + 2 )}{2}

= [\frac{sec ^{4} ( x ) sin ( x )}{4}]_{0}^{\frac{π}{4}} + \frac{3}{4} \cdot \frac{2 + ln ( 1 + 2 )}{2}

Vereinfache

[\frac{sec ^{4} ( x ) sin ( x )}{4}]_{0}^{\frac{π}{4}} + \frac{3}{4} \cdot \frac{2 + ln ( 1 + 2 )}{2} : [\frac{1}{4} sec^{4} (x) sin (x)]_{0}^{\frac{π}{4}} + \frac{3 ( 2 + ln ( 1 + 2 ) )}{8}

= [\frac{1}{4} sec^{4} (x) sin (x)]_{0}^{\frac{π}{4}} + \frac{3 ( 2 + ln ( 1 + 2 ) )}{8}

Berechne die Grenzen:

\frac{1}{2}

= \frac{1}{2} + \frac{3 ( 2 + ln ( 1 + 2 ) )}{8}

Vereinfache

= \frac{3 2 ln ( 1 + 2 ) + 14}{8 2}

Graph

Beliebte Beispiele

derivative of 8(x+4^{3/2})

\frac{d}{d x} (8 (x + 4)^{\frac{3}{2}})

y^'=e^{x-y},y(0)=2

y^{^{'}} = e^{x - y}, y (0) = 2

limit as x approaches 2 of 5x-7

x \to 2 lim (5 x - 7)

limit as x approaches pi of ln|cos(x)-9|

x \to π lim (ln ∣ cos (x) - 9 ∣)

integral of 20-0.01x

\int 20 - 0.01 x d x