What is the integral of (e^x)^2x^2 ?

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

Popular >

integral of (e^x)^2x^2

integral

(e^{x})^{2} x^{2}

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

Solution steps

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

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

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

Apply Integration By Parts

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

= \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})

= \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

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

\frac{x ^{2}}{4 - x ^{2}}

\frac{1}{( 100 + x ^{2} )}

\frac{( r ^{2} )}{( 1 + r ^{2} ) d}

sin^{3} (2 x) cos (2 x)

(1 + 8 x)^{\frac{3}{2}}

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