What is the integral of 6x^2e^x ?

The integral of 6x^2e^x is 6(x^2e^x-2(e^xx-e^x))+C

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integral of 6x^2e^x

\int 6 x^{2} e^{x} d x

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

Solution steps

\int 6 x^{2} e^{x} d x

Take the constant out:

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

= 6 \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

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

= 6 (x^{2} e^{x} - \int 2 x e^{x} d x)

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

= 6 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Add a constant to the solution

= 6 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

\int \frac{u}{u - 1} d u

f (x) = x cos (x) sin (x)

\int_{0}^{1} \frac{1}{t ^{2} + 2} d t

x^{4} + y^{3} x^{5} + 4 \frac{d y}{d x} = 0

\int \frac{sin ( 3 x )}{cos ^{3} ( 3 x )} d x

What is the integral of 6x^2e^x ?
The integral of 6x^2e^x is 6(x^2e^x-2(e^xx-e^x))+C