integral of x(1-3x^2)^4

Lösung

\int x (1 - 3 x^{2})^{4} d x

- \frac{1}{30} (1 - 3 x^{2})^{5} + C

Schritte zur Lösung

\int x (1 - 3 x^{2})^{4} d x

Wende U-Substitution an

= \int - \frac{u ^{4}}{6} d u

Entferne die Konstante:

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

= - \frac{1}{6} \cdot \int u^{4} d u

Wende die Potenzregel an

= - \frac{1}{6} \cdot \frac{u ^{5}}{5}

Setze in

u = 1 - 3 x^{2}

ein

= - \frac{1}{6} \cdot \frac{( 1 - 3 x ^{2} ) ^{5}}{5}

Vereinfache

- \frac{1}{6} \cdot \frac{( 1 - 3 x ^{2} ) ^{5}}{5} : - \frac{1}{30} (1 - 3 x^{2})^{5}

= - \frac{1}{30} (1 - 3 x^{2})^{5}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{30} (1 - 3 x^{2})^{5} + C

d er i v a t i v e ln (x) \cdot x

\frac{\partial}{\partial u} (4 sin (u) cos (v))

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

x \to 0 + lim (tan (2 x))

t an g e n t (8 x + 9)^{- 2}