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Beliebt Rechnen >

integral of cos^2(x)ln(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{2} ln (x) (x + \frac{1}{2} sin (2 x)) - \int \frac{2 x + sin ( 2 x )}{4 x} d x

\int \frac{2 x + sin ( 2 x )}{4 x} d x = \frac{1}{4} (2 x + Si (2 x))

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

Füge eine Konstante zur Lösung hinzu

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

Beliebte Beispiele

f(x)=(1+x+x^2)^{99}

f (x) = (1 + x + x^{2})^{99}

integral of 1-cos^2(x)

\int 1 - cos^{2} (x) d x

integral of 1/(x^{1.5)}

\int \frac{1}{x ^{1.5}} d x

f(x)=2cos(sin(x))

f (x) = 2 cos (sin (x))

(dy)/(dt)-7/t y=t^5

\frac{d y}{d t} - \frac{7}{t} y = t^{5}