What is the integral of (9te^t,ln(t)) ?

The integral of (9te^t,ln(t)) is 9,(ln(t)(e^tt-e^t)-(e^t-\Ei(t)))+C

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integral of (9te^t,ln(t))

\int (9 t e^{t}, ln (t)) d t

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

Solution steps

\int 9 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

= 9, \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

= 9, (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)

= 9, (ln (t) (e^{t} t - e^{t}) - (e^{t} - Ei (t)))

Add a constant to the solution

= 9, (ln (t) (e^{t} t - e^{t}) - (e^{t} - Ei (t))) + C

\frac{d}{d x} (\frac{sec ( x )}{tan ( x )})

6 y^{^{''}} + 4 y^{^{'}} = 0

x \to 5 - lim ((5 - x)^{\frac{2}{3}})

\int - \frac{7}{x} d x

x \to 4 lim (x^{3} - 64)

What is the integral of (9te^t,ln(t)) ?
The integral of (9te^t,ln(t)) is 9,(ln(t)(e^tt-e^t)-(e^t-\Ei(t)))+C