What is the integral from 0 to 7 of 8x*\sqrt[3]{x+1} ?

The integral from 0 to 7 of 8x*\sqrt[3]{x+1} is 2418/7

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integral from 0 to 7 of 8x*\sqrt[3]{x+1}

\frac{2418}{7}

Decimal

345.42857 \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}

= 8 (\frac{381}{7} - \frac{45}{4})

Simplify

8 (\frac{381}{7} - \frac{45}{4}) : \frac{2418}{7}

= \frac{2418}{7}

What is the integral from 0 to 7 of 8x*\sqrt[3]{x+1} ?
The integral from 0 to 7 of 8x*\sqrt[3]{x+1} is 2418/7