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 9tan^3(x)

Lösung

\int_{0}^{\frac{π}{4}} 9 tan^{3} (x) d x

Lösung

9 (- \frac{1}{2} ln (2) + \frac{1}{2})

+1

Dezimale

1.38083 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} 9 tan^{3} (x) d x

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{\frac{π}{4}} tan^{3} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 9 \cdot \int_{0}^{\frac{π}{4}} (- 1 + sec^{2} (x)) tan (x) d x

Wende U-Substitution an

= 9 \cdot \int_{1}^{2} \frac{- 1 + u ^{2}}{u} d u

Multipliziere aus

\frac{- 1 + u ^{2}}{u} : - \frac{1}{u} + u

= 9 \cdot \int_{1}^{2} - \frac{1}{u} + u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 9 (- \int_{1}^{2} \frac{1}{u} d u + \int_{1}^{2} u d u)

\int_{1}^{2} \frac{1}{u} d u = \frac{1}{2} ln (2)

\int_{1}^{2} u d u = \frac{1}{2}

= 9 (- \frac{1}{2} ln (2) + \frac{1}{2})

Graph

Beliebte Beispiele

derivative of (5x^4+3x^3/(4x-9))

\frac{d}{d x} (\frac{5 x ^{4} + 3 x ^{3}}{4 x - 9})

maclaurin e^xsin(x)

ma c l a u r in e^{x} sin (x)

integral of (5-e^x)/(e^{2x)}

\int \frac{5 - e ^{x}}{e ^{2 x}} d x

integral of 1/((64-x^2)^{3/2)}

\int \frac{1}{( 64 - x ^{2} ) ^{\frac{3}{2}}} d x

derivative (220x)/((x+2)^2)

d er i v a t i v e \frac{220 x}{( x + 2 ) ^{2}}