integral of x^2-ln(x^2)+k

Lösung

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

\frac{x ^{3}}{3} - 2 x ln (x) + 2 x + k x + C

Schritte zur Lösung

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

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

\int ln (x^{2}) d x = 2 x ln (x) - 2 x

\int k d x = k x

= \frac{x ^{3}}{3} - (2 x ln (x) - 2 x) + k x

Vereinfache

= \frac{x ^{3}}{3} - 2 x ln (x) + 2 x + k x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - 2 x ln (x) + 2 x + k x + C

\int_{1}^{5} 1 d x

\int x^{2} \cdot e^{- a x} d x

t a y l or \frac{1}{( x - 1 )}

x \to 2 lim (ln (\frac{x}{x ^{2} - 4}))

d er i v a t i v e a y (e^{b y})