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Beliebt Rechnen >

integral of 3x(x^2-1/3)

Lösung

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

Lösung

3 (\frac{1}{6} x^{2} (3 x^{2} - 1) - \frac{x ^{4}}{4}) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= 3 (\frac{1}{6} x^{2} (3 x^{2} - 1) - \int x^{3} d x)

\int x^{3} d x = \frac{x ^{4}}{4}

= 3 (\frac{1}{6} x^{2} (3 x^{2} - 1) - \frac{x ^{4}}{4})

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{1}{6} x^{2} (3 x^{2} - 1) - \frac{x ^{4}}{4}) + C

Graph

Beliebte Beispiele

tangent f(x)= x/(x+1),\at x=-2

t an g e n t f (x) = \frac{x}{x + 1}, at x = - 2

(\partial)/(\partial x)(-1/(2x^2))

\frac{\partial}{\partial x} (- \frac{1}{2 x ^{2}})

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

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

derivative of sin^{-1}(x)

\frac{d}{d x} (sin^{- 1} (x))

integral of sec^2(X)

\int sec^{2} (X) d X