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Beliebt Rechnen >

integral of sin(t)e^t

Lösung

\int sin (t) e^{t} d t

Lösung

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

Schritte zur Lösung

\int sin (t) e^{t} d t

Wende die partielle Integration an

= - e^{t} cos (t) - \int - e^{t} cos (t) d t

Entferne die Konstante:

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

= - e^{t} cos (t) - (- \int e^{t} cos (t) d t)

Wende die partielle Integration an

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

Deshalb

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

Isoliere

\int e^{t} sin (t) d t

= - \frac{e ^{t} cos ( t )}{2} + \frac{e ^{t} sin ( t )}{2}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

inverselaplace (12)/(3s-5)

in v erse l a pl a ce \frac{12}{3 s - 5}

(d^2)/(dx^2)((6pi^2)/(6-x))

\frac{d ^{2}}{d x ^{2}} (\frac{6 π ^{2}}{6 - x})

sum from n=5 to infinity of (8^n)/(9^n)

n = 5 \sum \infty \frac{8 ^{n}}{9 ^{n}}

integral of 3/5-4/x

\int \frac{3}{5} - \frac{4}{x} d x

sum from n=1 to infinity of n(sin(1/n))

n = 1 \sum \infty n (sin (\frac{1}{n}))