integral of sin(ln(x^2))

Lösung

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

\frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x)) + C

Schritte zur Lösung

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

Vereinfache

ln (x^{2}) : 2 ln (x)

= \int sin (2 ln (x)) d x

Wende die partielle Integration an

= x sin (2 ln (x)) - \int 2 cos (2 ln (x)) d x

\int 2 cos (2 ln (x)) d x = 2 (\frac{2}{5} x sin (2 ln (x)) + \frac{1}{5} x cos (2 ln (x)))

= x sin (2 ln (x)) - 2 (\frac{2}{5} x sin (2 ln (x)) + \frac{1}{5} x cos (2 ln (x)))

Vereinfache

x sin (2 ln (x)) - 2 (\frac{2}{5} x sin (2 ln (x)) + \frac{1}{5} x cos (2 ln (x))) : \frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x))

= \frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x)) + C

(5 x^{2} + 3 y + 3 y^{2}) d x + (x + 2 x y) d y = 0

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

\frac{d y}{d x} - y = x y^{5}

\int 14 cos^{3} (x) d x

\int (2 x + 1) d x