What is the integral of (3te^t,ln(t)) ?

The integral of (3te^t,ln(t)) is 3,(ln(t)(e^tt-e^t)-(e^t-\Ei(t)))+C

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: ln (t) (e^{t} t - e^{t}) - \int \frac{e ^{t} t - e ^{t}}{t} d t

= 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)))

Add a constant to the solution

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

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

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

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

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

\int 6 sin (x) d x

What is the integral of (3te^t,ln(t)) ?
The integral of (3te^t,ln(t)) is 3,(ln(t)(e^tt-e^t)-(e^t-\Ei(t)))+C