integral of (x^2+7)*ln(x)

Lösung

\int (x^{2} + 7) \cdot ln (x) d x

ln (x) (\frac{x ^{3}}{3} + 7 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 21 x) + C

Schritte zur Lösung

\int (x^{2} + 7) ln (x) d x

Wende die partielle Integration an

= ln (x) (\frac{x ^{3}}{3} + 7 x) - \int \frac{1}{3} (x^{2} + 21) d x

\int \frac{1}{3} (x^{2} + 21) d x = \frac{1}{3} (\frac{x ^{3}}{3} + 21 x)

= ln (x) (\frac{x ^{3}}{3} + 7 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 21 x)

Füge eine Konstante zur Lösung hinzu

= ln (x) (\frac{x ^{3}}{3} + 7 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 21 x) + C

x \to 0 lim (\frac{1}{cos ( 19 x )})

\int (2 x + 1) (2 x - 1) d x

d er i v a t i v e f (x) = \frac{e ^{- x}}{x}

\int \frac{cos ( x ^{2} )}{x} d x

d er i v a t i v e (\frac{1}{2})^{x - 1} + 3