integral of (ln(sin(x)))/(sin^2(x))

Lösung

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

- ln (sin (x)) cot (x) - x - cot (x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - cot^{2} (x) d x = x + cot (x)

= - ln (sin (x)) cot (x) - (x + cot (x))

Vereinfache

= - ln (sin (x)) cot (x) - x - cot (x)

Füge eine Konstante zur Lösung hinzu

= - ln (sin (x)) cot (x) - x - cot (x) + C

\frac{\partial}{\partial x} (x^{2} + y^{2} - y^{2} x - 7)

t an g e n t f (x) = x^{2} - 2, (3, 7)

x \to 0 lim ((c e^{x} + 1) i f)

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

\frac{d}{d x} (\frac{x ^{4}}{4} + \frac{1}{8 x ^{2}})