integral of sin(x)ln(sin(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - cot (x) cos (x) d x = - ln tan (\frac{x}{2}) - cos (x)

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

t an g e n t x^{6}, at x = 3

x \to 0 lim (\frac{x}{x - 1})

d er i v a t i v e \frac{cos ( x )}{x ^{4}}

\frac{d}{d x} (5 x + 7)

d er i v a t i v e \frac{ln ( x )}{x}