What is the integral of 4x*e^x ?

The integral of 4x*e^x is 4(e^xx-e^x)+C

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integral of 4x*e^x

\int 4 x \cdot e^{x} d x

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

Solution steps

\int 4 x e^{x} d x

Take the constant out:

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

= 4 \cdot \int x e^{x} d x

Apply Integration By Parts

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

= 4 (e^{x} x - \int e^{x} d x)

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

= 4 (e^{x} x - e^{x})

Add a constant to the solution

= 4 (e^{x} x - e^{x}) + C

\frac{\partial}{\partial x} (- \frac{9 x}{y})

- x^{^{'}} - \frac{x}{0.00022} + 13364 = 0

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

\int \frac{a + b x ^{8}}{9 a x + b x ^{9}} d x

x \to \infty lim (b^{x})