integral of x^{11}ln(5x^6)

Lösung

\int x^{11} ln (5 x^{6}) d x

\frac{1}{12} x^{12} (ln (5) + 6 ln (x)) - \frac{x ^{12}}{24} + C

Schritte zur Lösung

\int x^{11} ln (5 x^{6}) d x

Wende die partielle Integration an

= \frac{1}{12} x^{12} ln (5 x^{6}) - \int \frac{x ^{11}}{2} d x

\int \frac{x ^{11}}{2} d x = \frac{x ^{12}}{24}

= \frac{1}{12} x^{12} ln (5 x^{6}) - \frac{x ^{12}}{24}

Vereinfache

ln (5 x^{6}) : 6 ln (x) + ln (5)

= \frac{1}{12} x^{12} (ln (5) + 6 ln (x)) - \frac{x ^{12}}{24}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} x^{12} (ln (5) + 6 ln (x)) - \frac{x ^{12}}{24} + C

\int (x^{2} y^{3}) d x

\int 5 x^{4} cos (x^{5}) d x

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

\int (9 + tan^{2} (θ)) d θ

\int 6 x 4 + x^{2} d x