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

\int e^{2 x} \cdot 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

\frac{\partial}{\partial x} (4 (y^{2} - x^{2}) ln (x + y))

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

\frac{1}{2 x} - \frac{8}{5 x ^{4}}

\int \frac{lo g _{e} ( x )}{x} d x

f (x) = ln (10 x)

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