What is the integral of 5x^2e^x ?

The integral of 5x^2e^x is 5(x^2e^x-2(e^xx-e^x))+C

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integral of 5x^2e^x

\int 5 x^{2} e^{x} d x

5 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

Solution steps

\int 5 x^{2} e^{x} d x

Take the constant out:

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

= 5 \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

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

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

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

= 5 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Add a constant to the solution

= 5 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

(x + \frac{2 y ^{2}}{x}) d x = y d y

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

f (t) = (3 t + 14)^{\frac{2}{3}}

\frac{d y}{d x} + \frac{y}{x ^{2} + x} = x + 1

\frac{d}{d x} (2 I n x)

What is the integral of 5x^2e^x ?
The integral of 5x^2e^x is 5(x^2e^x-2(e^xx-e^x))+C