What is the integral of (7x^2)/(e^x) ?

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

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integral of (7x^2)/(e^x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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