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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{a} sin^{3} (a x) - \frac{2}{3 a} sin^{3} (a x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{a} sin^{3} (a x) - \int sin (a x) sin (2 a x) d x

\int sin (a x) sin (2 a x) d x = \frac{2}{3 a} sin^{3} (a x)

= \frac{1}{a} sin^{3} (a x) - \frac{2}{3 a} sin^{3} (a x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{a} sin^{3} (a x) - \frac{2}{3 a} sin^{3} (a x) + C

Graph

Beliebte Beispiele

integral of (3-x)^{1/2}

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

integral of 2x^3-2x^2+2x-10

\int 2 x^{3} - 2 x^{2} + 2 x - 10 d x

integral of 1/((2x-7)^4)

\int \frac{1}{( 2 x - 7 ) ^{4}} d x

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

\int \frac{arctan ^{2} ( x )}{x ^{2} + 1} d x

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

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