What is the integral from 1 to 1024 of (e^{\sqrt[5]{x}})/(\sqrt[5]{x^4)} ?

The integral from 1 to 1024 of (e^{\sqrt[5]{x}})/(\sqrt[5]{x^4)} is 5(e^4-e)

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integral from 1 to 1024 of (e^{\sqrt[5]{x}})/(\sqrt[5]{x^4)}

\int_{1}^{1024} \frac{e ^{5 x}}{5 x ^{4}} d x

5 (e^{4} - e)

Decimal

259.39934 \dots

Solution steps

\int_{1}^{1024} \frac{e ^{5 x}}{5 x ^{4}} d x

Apply u-substitution

: \int_{1}^{4} 5 e^{u} d u

= \int_{1}^{4} 5 e^{u} d u

Take the constant out:

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

= 5 \cdot \int_{1}^{4} e^{u} d u

Use the common integral:

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

= 5 [e^{u}]_{1}^{4}

Compute the boundaries:

e^{4} - e

= 5 (e^{4} - e)

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What is the integral from 1 to 1024 of (e^{\sqrt[5]{x}})/(\sqrt[5]{x^4)} ?
The integral from 1 to 1024 of (e^{\sqrt[5]{x}})/(\sqrt[5]{x^4)} is 5(e^4-e)