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Beliebt Rechnen >

integral (sin^4(x))/(cos^2(x))

Lösung

integral

\frac{sin ^{4} ( x )}{cos ^{2} ( x )}

Lösung

sin^{3} (x) cos (x) - \frac{3}{2} x + \frac{3}{4} sin (2 x) + sin^{4} (x) tan (x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= - \int 4 sin^{4} (x) d x + sin^{4} (x) tan (x)

\int 4 sin^{4} (x) d x = - sin^{3} (x) cos (x) + \frac{3}{2} x - \frac{3}{4} sin (2 x)

= - (- sin^{3} (x) cos (x) + \frac{3}{2} x - \frac{3}{4} sin (2 x)) + sin^{4} (x) tan (x)

Vereinfache

= sin^{3} (x) cos (x) - \frac{3}{2} x + \frac{3}{4} sin (2 x) + sin^{4} (x) tan (x)

Füge eine Konstante zur Lösung hinzu

= sin^{3} (x) cos (x) - \frac{3}{2} x + \frac{3}{4} sin (2 x) + sin^{4} (x) tan (x) + C

Graph

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