de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of csc^3(2t-3)

Lösung

\int csc^{3} (2 t - 3) d t

Lösung

\frac{1}{16} (- cot^{2} (\frac{2 t - 3}{2}) + 4 ln tan (\frac{2 t - 3}{2}) + tan^{2} (\frac{2 t - 3}{2})) + C

Schritte zur Lösung

\int csc^{3} (2 t - 3) d t

Wende U-Substitution an

= \int csc^{3} (u) \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int csc^{3} (u) d u

Wende U-Substitution an

= \frac{1}{2} \cdot \int \frac{( 1 + v ^{2} ) ^{2}}{4 v ^{3}} d v

Entferne die Konstante:

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

= \frac{1}{2} \cdot \frac{1}{4} \cdot \int \frac{( 1 + v ^{2} ) ^{2}}{v ^{3}} d v

Multipliziere aus

\frac{( 1 + v ^{2} ) ^{2}}{v ^{3}} : \frac{1}{v ^{3}} + \frac{2}{v} + v

= \frac{1}{2} \cdot \frac{1}{4} \cdot \int \frac{1}{v ^{3}} + \frac{2}{v} + v d v

Wende die Summenregel an:

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

= \frac{1}{2} \cdot \frac{1}{4} (\int \frac{1}{v ^{3}} d v + \int \frac{2}{v} d v + \int v d v)

\int \frac{1}{v ^{3}} d v = - \frac{1}{2 v ^{2}}

\int \frac{2}{v} d v = 2 ln ∣ v ∣

\int v d v = \frac{v ^{2}}{2}

= \frac{1}{2} \cdot \frac{1}{4} (- \frac{1}{2 v ^{2}} + 2 ln ∣ v ∣ + \frac{v ^{2}}{2})

Ersetze zurück

= \frac{1}{2} \cdot \frac{1}{4} (- \frac{1}{2 tan ^{2} ( \frac{2 t - 3}{2} )} + 2 ln tan (\frac{2 t - 3}{2}) + \frac{tan ^{2} ( \frac{2 t - 3}{2} )}{2})

Vereinfache

\frac{1}{2} \cdot \frac{1}{4} (- \frac{1}{2 tan ^{2} ( \frac{2 t - 3}{2} )} + 2 ln tan (\frac{2 t - 3}{2}) + \frac{tan ^{2} ( \frac{2 t - 3}{2} )}{2}) : \frac{1}{16} (- cot^{2} (\frac{2 t - 3}{2}) + 4 ln tan (\frac{2 t - 3}{2}) + tan^{2} (\frac{2 t - 3}{2}))

= \frac{1}{16} (- cot^{2} (\frac{2 t - 3}{2}) + 4 ln tan (\frac{2 t - 3}{2}) + tan^{2} (\frac{2 t - 3}{2}))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{16} (- cot^{2} (\frac{2 t - 3}{2}) + 4 ln tan (\frac{2 t - 3}{2}) + tan^{2} (\frac{2 t - 3}{2})) + C

Graph

Beliebte Beispiele

integral of 2βx(1-x^2)^{β-1}

\int 2 β x (1 - x^{2})^{β - 1} d x

integral of sin(3x)*e^{-x}

\int sin (3 x) \cdot e^{- x} d x

integral of (sin(2t))

\int (sin (2 t)) d t

integral of 1/((x+9)^8)

\int \frac{1}{( x + 9 ) ^{8}} d x

integral of (2x-5sqrt(x))^2

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