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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int u ln (u) d u

Wende die partielle Integration an

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

\int \frac{u}{2} d u = \frac{u ^{2}}{4}

= \frac{1}{2} u^{2} ln (u) - \frac{u ^{2}}{4}

Setze in

u = sin (x)

ein

= \frac{1}{2} sin^{2} (x) ln (sin (x)) - \frac{sin ^{2} ( x )}{4}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral from 0 to 1 of sqrt(4-x^2)

\int_{0}^{1} 4 - x^{2} d x

integral of 9/(x^4)

\int \frac{9}{x ^{4}} d x

fläche 7x-x^2,2x

a re a 7 x - x^{2}, 2 x

derivative f(x)= 1/2 (x+1)^{-1/2}

d er i v a t i v e f (x) = \frac{1}{2} (x + 1)^{- \frac{1}{2}}

derivative e^{cos(3x)}

d er i v a t i v e e^{c o s (3 x)}