What is the integral of (e^{2x}x^2) ?

The integral of (e^{2x}x^2) is 1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x})+C

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integral of e^(2x)x^2 with respect to x

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

\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

Solution steps

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

Apply Integration By Parts

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

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

\int e^{2 x} x d x = \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})

= \frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})

Add a constant to the solution

= \frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

n = 1 \sum \infty (\frac{- 1}{3})^{n - 1}

x \to 0 lim (\frac{( sin ( cos ( x ) ) )}{( sec ( x ) )})

- \frac{d}{d t} (sin (2 t))

- \frac{d}{d x} y = 3 e^{x}

- \frac{d}{d t} (2 t)

What is the integral of (e^{2x}x^2) ?
The integral of (e^{2x}x^2) is 1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x})+C