What is the integral from 0 to 1 of x^2sqrt(e^x) ?

The integral from 0 to 1 of x^2sqrt(e^x) is 10sqrt(e)-16

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integral from 0 to 1 of x^2sqrt(e^x)

\int_{0}^{1} x^{2} e^{x} d x

10 e - 16

Solution steps

\int_{0}^{1} x^{2} e^{x} d x

Apply Integration By Parts

: [2 e^{\frac{x}{2}} x^{2} - \int 4 e^{\frac{x}{2}} x d x]_{0}^{1}

= [2 e^{\frac{x}{2}} x^{2} - \int 4 e^{\frac{x}{2}} x d x]_{0}^{1}

\int 4 e^{\frac{x}{2}} x d x = 16 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}})

= [2 e^{\frac{x}{2}} x^{2} - 16 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}})]_{0}^{1}

Compute the boundaries:

10 e - 16

= 10 e - 16

\int_{0}^{1} 4 y^{4} d y

\int_{1}^{10} \frac{1}{t} d t

\int_{- 3}^{1} \frac{4}{x ^{4}} d x

\int_{1}^{3} 0.2 e^{0.2 t} d t

What is the integral from 0 to 1 of x^2sqrt(e^x) ?
The integral from 0 to 1 of x^2sqrt(e^x) is 10sqrt(e)-16