What is the integral of xe^xln(2) ?

The integral of xe^xln(2) is ln(2)(e^xx-e^x)+C

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integral of xe^xln(2)

\int x e^{x} ln (2) d x

ln (2) (e^{x} x - e^{x}) + C

Solution steps

\int x e^{x} ln (2) d x

Take the constant out:

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

= ln (2) \cdot \int x e^{x} d x

Apply Integration By Parts

: e^{x} x - \int e^{x} d x

= ln (2) (e^{x} x - \int e^{x} d x)

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

= ln (2) (e^{x} x - e^{x})

Add a constant to the solution

= ln (2) (e^{x} x - e^{x}) + C

\int x - x^{\frac{1}{2}} d x

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\int 5 x \cdot cos (x) d x

\int (x ln (x) + \frac{1}{x ( x ^{2} + 1 )}) d x

What is the integral of xe^xln(2) ?
The integral of xe^xln(2) is ln(2)(e^xx-e^x)+C