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

解

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

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

解答ステップ

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

定数を除く:

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

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

部分積分を適用する

= 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)))

定数を解答に追加する

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