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Beliebt Rechnen >

integral of sin(x)cos^7(x)

Lösung

\int sin (x) cos^{7} (x) d x

Lösung

- \frac{cos ^{8} ( x )}{8} + C

Schritte zur Lösung

\int sin (x) cos^{7} (x) d x

Wende U-Substitution an

= \int - u^{7} d u

Entferne die Konstante:

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

= - \int u^{7} d u

Wende die Potenzregel an

= - \frac{u ^{8}}{8}

Setze in

u = cos (x)

ein

= - \frac{cos ^{8} ( x )}{8}

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ^{8} ( x )}{8} + C

Graph

Beliebte Beispiele

derivative of 24sqrt(x)

\frac{d}{d x} (24 x)

(\partial)/(\partial x)((xy)/(6x+7y))

\frac{\partial}{\partial x} (\frac{x y}{6 x + 7 y})

integral of sqrt(x^2+2x-8)

\int x^{2} + 2 x - 8 d x

integral of (cos(1/(x^2)))/(x^3)

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

integral from 0 to 9 of f(x)

\int_{0}^{9} f (x) d x