What is the integral of (5x^2)/(e^x) ?

The integral of (5x^2)/(e^x) is 5(-(x^2)/(e^x)+2(-x/(e^x)-1/(e^x)))+C

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integral of (5x^2)/(e^x)

\int \frac{5 x ^{2}}{e ^{x}} d x

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

Solution steps

\int \frac{5 x ^{2}}{e ^{x}} d x

Take the constant out:

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

= 5 \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

= 5 (- \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}})

= 5 (- \frac{x ^{2}}{e ^{x}} - (- 2 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})))

Simplify

= 5 (- \frac{x ^{2}}{e ^{x}} + 2 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}))

Add a constant to the solution

= 5 (- \frac{x ^{2}}{e ^{x}} + 2 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})) + C

\frac{\partial}{\partial x} (e^{- 2 t} cos (2 x))

\frac{\partial}{\partial x} (sec (x) tan (x))

y^{^{'}} = 5 y^{\frac{1}{5}}

\frac{d}{d x} (3 x + \frac{6}{x})

\frac{d}{d x} (\frac{1}{2} sin (x))

What is the integral of (5x^2)/(e^x) ?
The integral of (5x^2)/(e^x) is 5(-(x^2)/(e^x)+2(-x/(e^x)-1/(e^x)))+C