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Beliebt Rechnen >

integral of (1-sin^3(x))/(sin^2(x))

Lösung

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

Lösung

- cot (x) + cos (x) + C

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int sin (x) d x = - cos (x)

= - cot (x) - (- cos (x))

Vereinfache

= - cot (x) + cos (x)

Füge eine Konstante zur Lösung hinzu

= - cot (x) + cos (x) + C

Graph

Beliebte Beispiele

derivative of (2x^2-3x+1/x)

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

steigung x^2+xy+2y^2=28,(2,3)

s l o p e x^{2} + x y + 2 y^{2} = 28, (2, 3)

t^2y^{''}+7ty^'+10y=0

t^{2} y^{^{''}} + 7 t y^{^{'}} + 10 y = 0

integral of tan(4x)sec^5(4x)

\int tan (4 x) sec^{5} (4 x) d x

limit as x approaches 7-of 1/(x-7)

x \to 7 - lim (\frac{1}{x - 7})