What is the integral of e^x*2x ?

The integral of e^x*2x is 2(e^xx-e^x)+C

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integral of e^x*2x

\int e^{x} \cdot 2 x d x

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

Solution steps

\int e^{x} \cdot 2 x d x

Take the constant out:

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

= 2 \cdot \int e^{x} x d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{t ^{2}}{1 + t ^{6}} d t

\frac{w}{w + \frac{c}{w}}

y = x^{2} - 6, at x = a

\frac{x ^{2} - 4}{x - 3}

\frac{d}{d θ} (1 - 2 sin (θ))