What is the integral of 9x^2e^{2x} ?

The integral of 9x^2e^{2x} is 9(1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x}))+C

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integral of 9x^2e^{2x}

\int 9 x^{2} e^{2 x} d x

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

Solution steps

\int 9 x^{2} e^{2 x} d x

Take the constant out:

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

= 9 \cdot \int x^{2} e^{2 x} d x

Apply Integration By Parts

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

= 9 (\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})

= 9 (\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

= 9 (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})) + C

t \to 0 lim (I (t) n t)

\int_{2}^{\infty} - 2 x^{- 2} d x

\frac{d}{d x} (\frac{2}{4 x - 3})

\int \frac{t ^{3}}{a ^{4} + t ^{4}} d t

\frac{d}{d x} (arctan (7 x))

What is the integral of 9x^2e^{2x} ?
The integral of 9x^2e^{2x} is 9(1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x}))+C