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Beliebt Rechnen >

integral of cos^2(ln(x))

Lösung

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

Lösung

\frac{1}{10} (5 x + 2 x sin (2 ln (x)) + x cos (2 ln (x))) + C

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

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

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

Vereinfache

\frac{1}{2} (x + \frac{2}{5} x sin (2 ln (x)) + \frac{1}{5} x cos (2 ln (x))) : \frac{1}{10} (5 x + 2 x sin (2 ln (x)) + x cos (2 ln (x)))

= \frac{1}{10} (5 x + 2 x sin (2 ln (x)) + x cos (2 ln (x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{10} (5 x + 2 x sin (2 ln (x)) + x cos (2 ln (x))) + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(y+(1/(1/x+1/z)))

\frac{\partial}{\partial x} (y + (\frac{1}{\frac{1}{x} + \frac{1}{z}}))

integral of x/(sqrt(1+x^2)+x)

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

limit as n approaches infinity of |n|

n \to \infty lim (∣ n ∣)

integral of e^{4/x}

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

fläche y=x,y= 1/(x^2),x=2

a re a y = x, y = \frac{1}{x ^{2}}, x = 2