integral of (x+1/x)x^2

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{1}{3} x (x^{2} - 1) d x = \frac{1}{3} (\frac{x ^{4}}{4} - \frac{x ^{2}}{2})

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

Füge eine Konstante zur Lösung hinzu

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

\int 5 x^{- 5} d x

\int cos (wt - B z) d t

\int \frac{1}{( x ^{2} - 9 ) ^{3}} d x

\int \frac{3 x + 2}{2 x + 1} d x

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