What is the integral of (x^2+1)/(e^x) ?

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

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integral of (x^2+1)/(e^x)

\int \frac{x ^{2} + 1}{e ^{x}} d x

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

Solution steps

\int \frac{x ^{2} + 1}{e ^{x}} d x

Apply Integration By Parts

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

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

Simplify

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

Add a constant to the solution

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

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