What is the integral from 0 to 7 of 5x\sqrt[3]{x+1} ?

The integral from 0 to 7 of 5x\sqrt[3]{x+1} is 6045/28

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integral from 0 to 7 of 5x\sqrt[3]{x+1}

\frac{6045}{28}

Decimal Notation

215.89285 \dots

Solution steps

Take the constant out:

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

Apply u-substitution

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int_{1}^{8} u^{\frac{4}{3}} d u = \frac{381}{7}

= 5 (\frac{381}{7} - \frac{45}{4})

Simplify

5 (\frac{381}{7} - \frac{45}{4}) : \frac{6045}{28}

= \frac{6045}{28}

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What is the integral from 0 to 7 of 5x\sqrt[3]{x+1} ?
The integral from 0 to 7 of 5x\sqrt[3]{x+1} is 6045/28