de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^3)/(sqrt((11)^2-x^2))

Lösung

\int \frac{x ^{3}}{( 11 ) ^{2} - x ^{2}} d x

Lösung

\frac{1}{3} (121 - x^{2})^{\frac{3}{2}} - 121 121 - x^{2} + C

Schritte zur Lösung

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

Vereinfache

= \int \frac{x ^{3}}{121 - x ^{2}} d x

Wende U-Substitution an

= \int u^{2} - 121 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

= \int u^{2} d u - \int 121 d u

\int u^{2} d u = \frac{u ^{3}}{3}

\int 121 d u = 121 u

= \frac{u ^{3}}{3} - 121 u

Setze in

u = 121 - x^{2}

ein

= \frac{( 121 - x ^{2} ) ^{3}}{3} - 121 121 - x^{2}

Vereinfache

\frac{( 121 - x ^{2} ) ^{3}}{3} - 121 121 - x^{2} : \frac{1}{3} (121 - x^{2})^{\frac{3}{2}} - 121 121 - x^{2}

= \frac{1}{3} (121 - x^{2})^{\frac{3}{2}} - 121 121 - x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (121 - x^{2})^{\frac{3}{2}} - 121 121 - x^{2} + C

Graph

Beliebte Beispiele

integral of x^{-2}(2x^4+3x^2-2x^{-3})

\int x^{- 2} (2 x^{4} + 3 x^{2} - 2 x^{- 3}) d x

integral of (5x^4-4x^3+3x^2)

\int (5 x^{4} - 4 x^{3} + 3 x^{2}) d x

integral of 6/(sqrt(25-(x+5)^2))

\int \frac{6}{25 - ( x + 5 ) ^{2}} d x

integral of (7-2x)^{10}

\int (7 - 2 x)^{10} d x

integral of ((x^4))/(x^2+1)

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