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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int - u d u

Entferne die Konstante:

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

= - \int u d u

Wende die Potenzregel an

= - \frac{u ^{2}}{2}

Setze in

u = cos^{2} (x)

ein

= - \frac{( cos ^{2} ( x ) ) ^{2}}{2}

Vereinfache

- \frac{( cos ^{2} ( x ) ) ^{2}}{2} : - \frac{1}{2} cos^{4} (x)

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of x^3+2x^2-1

\frac{d}{d x} (x^{3} + 2 x^{2} - 1)

integral of x(1-x)^{99}

\int x (1 - x)^{99} d x

integral of x/(x^4+4x^2+5)

\int \frac{x}{x ^{4} + 4 x ^{2} + 5} d x

limit as x approaches 2+of (2-x)/(|x-2|)

x \to 2 + lim (\frac{2 - x}{∣ x - 2 ∣})

limit as t approaches 0 of (e^{1/t})/t

t \to 0 lim (\frac{e ^{\frac{1}{t}}}{t})