What is the integral of xe^xln(x-1) ?

The integral of xe^xln(x-1) is ln(x-1)(e^xx-e^x)-e^x+C

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integral of xe^xln(x-1)

\int x e^{x} ln (x - 1) d x

ln (x - 1) (e^{x} x - e^{x}) - e^{x} + C

Solution steps

\int x e^{x} ln (x - 1) d x

Apply Integration By Parts

: ln (x - 1) (e^{x} x - e^{x}) - \int e^{x} d x

= ln (x - 1) (e^{x} x - e^{x}) - \int e^{x} d x

\int e^{x} d x = e^{x}

= ln (x - 1) (e^{x} x - e^{x}) - e^{x}

Add a constant to the solution

= ln (x - 1) (e^{x} x - e^{x}) - e^{x} + C

\int \frac{sin ^{5} ( ln ( x ) )}{x} d x

x \to 0 lim (\frac{5 + x - 5}{2 x})

f (t) = e^{7 t s i n (2 t)}

f (x) = x (27 x^{- 2} + 2), at x = - 3

\frac{\partial}{\partial x} (\frac{x - 1}{x + 1})

What is the integral of xe^xln(x-1) ?
The integral of xe^xln(x-1) is ln(x-1)(e^xx-e^x)-e^x+C