integral of xsin^2(ln(x))

Lösung

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

\frac{1}{2} x^{2} sin^{2} (ln (x)) - \frac{1}{8} (x^{2} sin (2 ln (x)) - x^{2} cos (2 ln (x))) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{2} x^{2} sin^{2} (ln (x)) - \int \frac{1}{2} x sin (2 ln (x)) d x

\int \frac{1}{2} x sin (2 ln (x)) d x = \frac{1}{8} (x^{2} sin (2 ln (x)) - x^{2} cos (2 ln (x)))

= \frac{1}{2} x^{2} sin^{2} (ln (x)) - \frac{1}{8} (x^{2} sin (2 ln (x)) - x^{2} cos (2 ln (x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} sin^{2} (ln (x)) - \frac{1}{8} (x^{2} sin (2 ln (x)) - x^{2} cos (2 ln (x))) + C

\int \frac{8}{x} + 6 x d x

\int \frac{5}{x} - 6 e^{x} d x

\int - y^{- 1} d y

\int \frac{x ^{5} - 7}{x ^{2}} d x

\int 1 d e^{- x^{2}}