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Beliebt Rechnen >

integral of cos^3(t)-sin^2(t)cos(t)

Lösung

\int cos^{3} (t) - sin^{2} (t) cos (t) d t

Lösung

sin (t) - \frac{2}{3} sin^{3} (t) + C

Schritte zur Lösung

\int cos^{3} (t) - sin^{2} (t) cos (t) d t

Wende die Summenregel an:

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

= \int cos^{3} (t) d t - \int sin^{2} (t) cos (t) d t

\int cos^{3} (t) d t = sin (t) - \frac{sin ^{3} ( t )}{3}

\int sin^{2} (t) cos (t) d t = \frac{sin ^{3} ( t )}{3}

= sin (t) - \frac{sin ^{3} ( t )}{3} - \frac{sin ^{3} ( t )}{3}

Vereinfache

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

= sin (t) - \frac{2}{3} sin^{3} (t)

Füge eine Konstante zur Lösung hinzu

= sin (t) - \frac{2}{3} sin^{3} (t) + C

Graph

Beliebte Beispiele

derivative y=x^2-5x-6

d er i v a t i v e y = x^{2} - 5 x - 6

derivative f(x)=((x+9))/(x^2-7x+1)

d er i v a t i v e f (x) = \frac{( x + 9 )}{x ^{2} - 7 x + 1}

derivative g(x)= 7/(sqrt(x))

d er i v a t i v e g (x) = \frac{7}{x}

integral of (4x^5)/(sqrt(1-12x^6))

\int \frac{4 x ^{5}}{1 - 12 x ^{6}} d x

derivative 12x^3-18x^2

d er i v a t i v e 12 x^{3} - 18 x^{2}