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Beliebt Rechnen >

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

Lösung

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

Beliebte Beispiele

normal x-10y=1,(-9,3)

n or ma l x - 10 y = 1, (- 9, 3)

(d^{10})/(dx^{10)}(x^{10})

\frac{d ^{10}}{d x ^{10}} (x^{10})

(5 sin (x))^{^{'}}

integral from 1 to 4 of sqrt(1+(9x)/4)

\int_{1}^{4} 1 + \frac{9 x}{4} d x

(\partial)/(\partial y)(5x^2y+5xy^2)

\frac{\partial}{\partial y} (5 x^{2} y + 5 x y^{2})