What is the integral of x^2(e^x)^3 ?

The integral of x^2(e^x)^3 is 1/3 e^{3x}x^2-2/27 (3e^{3x}x-e^{3x})+C

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integral of x^2(e^x)^3

integral

x^{2} (e^{x})^{3}

\frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x}) + C

Solution steps

\int x^{2} (e^{x})^{3} d x

Apply Integration By Parts

: \frac{1}{3} e^{3 x} x^{2} - \int \frac{2}{3} e^{3 x} x d x

= \frac{1}{3} e^{3 x} x^{2} - \int \frac{2}{3} e^{3 x} x d x

\int \frac{2}{3} e^{3 x} x d x = \frac{2}{27} (3 e^{3 x} x - e^{3 x})

= \frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x})

Add a constant to the solution

= \frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x}) + C

n^{2}

1 + 16 x^{2}

\frac{( e ^{2 x} )}{x}

2 x^{3} (e^{x})^{2}

2 x^{3} \cdot e^{- x}

What is the integral of x^2(e^x)^3 ?
The integral of x^2(e^x)^3 is 1/3 e^{3x}x^2-2/27 (3e^{3x}x-e^{3x})+C