integral of x^2ln(4x)

Lösung

\int x^{2} ln (4 x) d x

\frac{1}{3} x^{3} ln (4 x) - \frac{x ^{3}}{9} + C

Schritte zur Lösung

\int x^{2} ln (4 x) d x

Wende die partielle Integration an

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

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= \frac{1}{3} x^{3} ln (4 x) - \frac{x ^{3}}{9}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} ln (4 x) - \frac{x ^{3}}{9} + C

x \to - \frac{π}{4} lim (sec (x))

x \to 1 lim (+ (\frac{1}{x ^{2} - 1}))

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

x \to 0 lim ((1 - 10 x)^{\frac{1}{x}})

x \to \infty + lim (x^{(3)} e^{(- x^{(2)})})