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Beliebt Rechnen >

integral of sin(x)in(cos(x))

Lösung

\int sin (x) in (cos (x)) d x

Lösung

\frac{in}{2} sin^{2} (x) + C

Schritte zur Lösung

\int sin (x) in cos (x) d x

Entferne die Konstante:

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

= in \cdot \int sin (x) cos (x) d x

Wende U-Substitution an

= in \cdot \int u d u

Wende die Potenzregel an

= in \frac{u ^{2}}{2}

Setze in

u = sin (x)

ein

= in \frac{sin ^{2} ( x )}{2}

Vereinfache

in \frac{sin ^{2} ( x )}{2} : \frac{in}{2} sin^{2} (x)

= \frac{in}{2} sin^{2} (x)

Füge eine Konstante zur Lösung hinzu

= \frac{in}{2} sin^{2} (x) + C

Graph

Beliebte Beispiele

derivative f(x)=8sec(x)tan(x)

d er i v a t i v e f (x) = 8 sec (x) tan (x)

tangent f(x)=x^2+1,(0,1)

t an g e n t f (x) = x^{2} + 1, (0, 1)

sum from n=5 to infinity of (3^n)/(12^n)

n = 5 \sum \infty \frac{3 ^{n}}{1 2 ^{n}}

tangent y=x^2-5

t an g e n t y = x^{2} - 5

limit as x approaches-1 of 4x^2-2x-6

x \to - 1 lim (4 x^{2} - 2 x - 6)