What is the integral of 7x^2e^{6x} ?

The integral of 7x^2e^{6x} is 7(1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x}))+C

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integral of 7x^2e^{6x}

\int 7 x^{2} e^{6 x} d x

7 (\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x})) + C

Solution steps

\int 7 x^{2} e^{6 x} d x

Take the constant out:

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

= 7 \cdot \int x^{2} e^{6 x} d x

Apply Integration By Parts

: \frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x

= 7 (\frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x)

\int \frac{1}{3} e^{6 x} x d x = \frac{1}{108} (6 e^{6 x} x - e^{6 x})

= 7 (\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x}))

Add a constant to the solution

= 7 (\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x})) + C

(x^{- 2} + x)^{- 3}

f (x) = (x + 2 sin (x))

\int \frac{x - 3}{3 - 4 x ^{2}} d x

(4 X - 1)^{2} (3 X - 1)^{- 2}

\frac{d y}{d x} = 8 x y

What is the integral of 7x^2e^{6x} ?
The integral of 7x^2e^{6x} is 7(1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x}))+C