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Beliebt Rechnen >

integral of (3te^t,ln(t))

Lösung

\int (3 t e^{t}, ln (t)) d t

Lösung

3, (ln (t) (e^{t} t - e^{t}) - (e^{t} - Ei (t))) + C

Schritte zur Lösung

\int 3 t e^{t}, ln (t) d t

Entferne die Konstante:

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

= 3, \int t e^{t} ln (t) d t

Wende die partielle Integration an

= 3, (ln (t) (e^{t} t - e^{t}) - \int \frac{e ^{t} t - e ^{t}}{t} d t)

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

= 3, (ln (t) (e^{t} t - e^{t}) - (e^{t} - Ei (t)))

Füge eine Konstante zur Lösung hinzu

= 3, (ln (t) (e^{t} t - e^{t}) - (e^{t} - Ei (t))) + C

Beliebte Beispiele

integral of (3x^2)/2-x-16.5

\int \frac{3 x ^{2}}{2} - x - 16.5 d x

2x^3(dy)/(dx)=y(2x^2-y^2)

2 x^{3} \frac{d y}{d x} = y (2 x^{2} - y^{2})

limit as x approaches 0 of (-6)/(x^7)

x \to 0 lim (\frac{- 6}{x ^{7}})

(d^2)/(dx^2)(3sin(x))

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

integral of 6sin(sqrt(x))

\int 6 sin (x) d x