integral of ln(5x^2)

Lösung

\int ln (5 x^{2}) d x

x (ln (5) + 2 ln (x)) - 2 x + C

Schritte zur Lösung

\int ln (5 x^{2}) d x

Wende die partielle Integration an

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

\int 2 d x = 2 x

= x ln (5 x^{2}) - 2 x

Vereinfache

ln (5 x^{2}) : 2 ln (x) + ln (5)

= x (ln (5) + 2 ln (x)) - 2 x

Füge eine Konstante zur Lösung hinzu

= x (ln (5) + 2 ln (x)) - 2 x + C

\int_{1}^{2} 3 4 x^{2} - 3 d x

a re a f (x) = 2 x, 1, 3

\int \frac{cos ( x )}{sin ^{2} ( x ) - 81} d x

x \to 0 + lim (e^{x})

\frac{d}{d x} (ln (cos (e^{x^{2} - s e c (x)})))