integral of x^6ln(x)+4xsin(3x)

Lösung

\int x^{6} ln (x) + 4 x sin (3 x) d x

\frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49} + 4 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)) + C

Schritte zur Lösung

\int x^{6} ln (x) + 4 x sin (3 x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{6} ln (x) d x + \int 4 x sin (3 x) d x

\int x^{6} ln (x) d x = \frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49}

\int 4 x sin (3 x) d x = 4 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x))

= \frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49} + 4 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49} + 4 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)) + C

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