integral of x^3ln(x^4)

Lösung

\int x^{3} ln (x^{4}) d x

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

Schritte zur Lösung

\int x^{3} ln (x^{4}) d x

Wende die partielle Integration an

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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

\frac{d}{d x} (\frac{e ^{x}}{sin ( x )})

d er i v a t i v e sec^{2} (x) - tan^{2} (x)

\frac{d}{d x} (sin (x) + \frac{1}{x})

n = 2 \sum \infty \frac{1}{n ^{n}}