integral of x^4ln(sqrt(x))

Lösung

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

\frac{1}{2} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

Schritte zur Lösung

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

Vereinfache

ln (x) : \frac{1}{2} ln (x)

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= \frac{1}{2} (\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}

= \frac{1}{2} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

\int \frac{x ^{3} + 4 x + 1}{x} d x

\int (6 x^{2} + 3 x + 5 x^{- 1} + 3) d x

\int \frac{5 ( - 3 r - 4 )}{r ^{5}} d r

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

in t e g r a l \frac{7 x ^{2} - 9 x + 1}{x}