What is the integral from-2 to 3 of x^3ln(e^x) ?

The integral from-2 to 3 of x^3ln(e^x) is 55

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integral from-2 to 3 of x^3ln(e^x)

\int_{- 2}^{3} x^{3} ln (e^{x}) d x

55

Solution steps

\int_{- 2}^{3} x^{3} ln (e^{x}) d x

Simplify

x^{3} ln (e^{x}) : x^{4}

= \int_{- 2}^{3} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{- 2}^{3}

= [\frac{x ^{5}}{5}]_{- 2}^{3}

Compute the boundaries:

55

= 55

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What is the integral from-2 to 3 of x^3ln(e^x) ?
The integral from-2 to 3 of x^3ln(e^x) is 55