What is the integral of 8x^2e^{2x} ?

The integral of 8x^2e^{2x} is 8(1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x}))+C

Popular >

integral of 8x^2e^{2x}

\int 8 x^{2} e^{2 x} d x

8 (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})) + C

Solution steps

\int 8 x^{2} e^{2 x} d x

Take the constant out:

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

= 8 \cdot \int x^{2} e^{2 x} d x

Apply Integration By Parts

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

= 8 (\frac{1}{2} e^{2 x} x^{2} - \int e^{2 x} x d x)

\int e^{2 x} x d x = \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})

= 8 (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}))

Add a constant to the solution

= 8 (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})) + C

\int \frac{1}{x + 2 + 3} d x

\int 2 x (4 x^{2} - 3)^{3} d x

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

\int (x^{9}) d x

\int \frac{( 2 x ^{3} + x ^{2} + 4 )}{( x ^{2} + 4 ) ^{2}} d x

What is the integral of 8x^2e^{2x} ?
The integral of 8x^2e^{2x} is 8(1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x}))+C