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Beliebt Rechnen >

integral of 1/2 xcos(4x^2)

Lösung

\int \frac{1}{2} x cos (4 x^{2}) d x

Lösung

\frac{1}{16} sin (4 x^{2}) + C

Schritte zur Lösung

\int \frac{1}{2} x cos (4 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 x cos (4 x^{2}) d x

Wende U-Substitution an

= \frac{1}{2} \cdot \int \frac{cos ( u )}{8} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \frac{1}{8} \cdot \int cos (u) d u

Nutze das gemeinsame Integral :

\int cos (u) d u = sin (u)

= \frac{1}{2} \cdot \frac{1}{8} sin (u)

Setze in

u = 4 x^{2}

ein

= \frac{1}{2} \cdot \frac{1}{8} sin (4 x^{2})

Vereinfache

\frac{1}{2} \cdot \frac{1}{8} sin (4 x^{2}) : \frac{1}{16} sin (4 x^{2})

= \frac{1}{16} sin (4 x^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{16} sin (4 x^{2}) + C

Graph

Beliebte Beispiele

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\int - 2 x + 6 x^{2} - 4 x^{3} + C d x

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

sum from n=1 to infinity of 1/n-1/(2n+1)

n = 1 \sum \infty \frac{1}{n} - \frac{1}{2 n + 1}

taylor sqrt(1-x^2),0

t a y l or 1 - x^{2}, 0

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