integral of (3x^2+ln(x))

Lösung

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

x^{3} + x ln (x) - x + C

Schritte zur Lösung

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

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

\int ln (x) d x = x ln (x) - x

= x^{3} + x ln (x) - x

Füge eine Konstante zur Lösung hinzu

= x^{3} + x ln (x) - x + C

\int_{- 5}^{5} \frac{y}{25 - y ^{2}} d y

d er i v a t i v e x^{3} (2 x - 1)^{7}

x \to 0 lim (x + 2)

\frac{d}{d x} (sin (x + 3) + (- cos (x - \frac{1}{2})))

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