What is the integral of x^2e^{x^3+2} ?

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

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integral of x^2e^{x^3+2}

\int x^{2} e^{x^{3} + 2} d x

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

Solution steps

\int x^{2} e^{x^{3} + 2} d x

Apply Integration By Parts

: \frac{1}{3} e^{x^{3} + 2} x^{3} - \int e^{x^{3} + 2} x^{5} d x

= \frac{1}{3} e^{x^{3} + 2} x^{3} - \int e^{x^{3} + 2} x^{5} d x

\int e^{x^{3} + 2} x^{5} d x = \frac{e ^{2}}{3} (e^{x^{3}} x^{3} - e^{x^{3}})

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

Add a constant to the solution

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

\frac{d}{d x} (- \frac{4}{1 - 4 x})

\frac{1}{x - 1}, x = 7

y = x^{3} - 2 x^{2} + x + 7

(arcsin (x))^{^{'}}

\frac{\partial}{\partial x} (tan (x) y)

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