integral of x^3ln(x)+cos(3x+2)

Lösung

\int x^{3} ln (x) + cos (3 x + 2) d x

\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16} + \frac{1}{3} sin (3 x + 2) + C

Schritte zur Lösung

\int x^{3} ln (x) + cos (3 x + 2) 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^{3} ln (x) d x + \int cos (3 x + 2) d x

\int x^{3} ln (x) d x = \frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}

\int cos (3 x + 2) d x = \frac{1}{3} sin (3 x + 2)

= \frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16} + \frac{1}{3} sin (3 x + 2)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16} + \frac{1}{3} sin (3 x + 2) + C

\int \frac{4 x ^{2}}{7 x ^{3} + 6} d x

\int \frac{4}{8 + 5 x} d x

\int 3 x e^{- 5 x} d x

\int \frac{12 + 6 x ^{4}}{x ^{3} + 9 x} d x

\int \frac{e ^{x}}{( e ^{x} - 3 ) ( e ^{x} + 4 )} d x