What is the integral from-3 to 2 of e^{u+3} ?

The integral from-3 to 2 of e^{u+3} is e^5-1

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integral from-3 to 2 of e^{u+3}

\int_{- 3}^{2} e^{u + 3} d u

e^{5} - 1

Decimal

147.41315 \dots

Solution steps

\int_{- 3}^{2} e^{u + 3} d u

e^{u + 3} = e^{3} e^{u}

= \int_{- 3}^{2} e^{3} e^{u} d u

Take the constant out:

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

= e^{3} \cdot \int_{- 3}^{2} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{3} [e^{u}]_{- 3}^{2}

Compute the boundaries:

e^{2} - \frac{1}{e ^{3}}

= e^{3} (e^{2} - \frac{1}{e ^{3}})

Simplify

= e^{5} - 1

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

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\int_{- 2}^{5} x^{2} d x

\int_{0}^{1} (8 x^{e} + 3 e^{x}) d x

What is the integral from-3 to 2 of e^{u+3} ?
The integral from-3 to 2 of e^{u+3} is e^5-1