integral of 50x^4ln(x)

Lösung

\int 50 x^{4} ln (x) d x

50 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

Schritte zur Lösung

\int 50 x^{4} ln (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 50 \cdot \int x^{4} ln (x) d x

Wende die partielle Integration an

= 50 (\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x)

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= 50 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

Füge eine Konstante zur Lösung hinzu

= 50 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

\int e^{- (1 + i w) t} d t

\int \frac{2}{π csc ( x ) - π sin ( x )} d x

\int \frac{2 x}{16 - 9 x ^{2}} d x

\int \frac{x ( x ^{2} + 4 )}{x ^{2} - 4} d x

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