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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{12} (x^{2} - 3)^{6} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u ^{5}}{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 u^{5} d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Setze in

u = x^{2} - 3

ein

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

Vereinfache

\frac{1}{2} \cdot \frac{( x ^{2} - 3 ) ^{6}}{6} : \frac{1}{12} (x^{2} - 3)^{6}

= \frac{1}{12} (x^{2} - 3)^{6}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} (x^{2} - 3)^{6} + C

Graph

Beliebte Beispiele

derivative of 3(x^2+y^2^2)

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

derivative y=4cot(3-2x)

d er i v a t i v e y = 4 cot (3 - 2 x)

integral from 0 to 2 of (4x-2x^2)

\int_{0}^{2} (4 x - 2 x^{2}) d x

(dy)/(dx)y=(x^2+3x)^2

\frac{d y}{d x} y = (x^{2} + 3 x)^{2}

limit as x approaches-infinity of 4/x

x \to - \infty lim (\frac{4}{x})