What is the integral of 3xe^x ?

The integral of 3xe^x is 3(e^xx-e^x)+C

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integral of 3xe^x

\int 3 x e^{x} d x

3 (e^{x} x - e^{x}) + C

Solution steps

\int 3 x e^{x} d x

Take the constant out:

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

= 3 \cdot \int x e^{x} d x

Apply Integration By Parts

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

= 3 (e^{x} x - \int e^{x} d x)

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

= 3 (e^{x} x - e^{x})

Add a constant to the solution

= 3 (e^{x} x - e^{x}) + C

x \to 0 lim (\frac{3 x ^{2} - 4 x}{x})

\int ln (2 x + 7) d x

\frac{d}{d x} ((sin (x))^{t a n (x)})

\int_{0}^{e} 2 π y (1 - ln (y)) d y

\frac{8}{x + 11}, at x = 5