integral of xsqrt(4-x^2)-x^2(sqrt(3))/3

Lösung

\int x 4 - x^{2} - x^{2} \frac{3}{3} d x

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

Schritte zur Lösung

\int x 4 - x^{2} - x^{2} \frac{3}{3} d x

Wende die Summenregel an:

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

= \int x 4 - x^{2} d x - \int x^{2} \frac{3}{3} d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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

d er i v a t i v e x 9 - x

\int tan (- 6 x + 3) d x

\int 8 sin^{2} (x co) s^{3} x d x

f (x) = \frac{x}{4 x - 3 ln ( x )}