What is the integral from 0 to 1 of x^3sqrt(7+5x^4) ?

The integral from 0 to 1 of x^3sqrt(7+5x^4) is (24sqrt(3)-7sqrt(7))/(30)

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integral from 0 to 1 of x^3sqrt(7+5x^4)

\int_{0}^{1} x^{3} 7 + 5 x^{4} d x

\frac{24 3 - 7 7}{30}

Decimal

0.76829 \dots

Solution steps

\int_{0}^{1} x^{3} 7 + 5 x^{4} d x

Apply u-substitution

: \int_{7}^{23} \frac{u ^{2}}{10} d u

= \int_{7}^{23} \frac{u ^{2}}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{7}^{23} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{7}^{23}

= \frac{1}{10} [\frac{u ^{3}}{3}]_{7}^{23}

Compute the boundaries:

83 - \frac{7 7}{3}

= \frac{1}{10} (83 - \frac{7 7}{3})

Simplify

= \frac{24 3 - 7 7}{30}

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What is the integral from 0 to 1 of x^3sqrt(7+5x^4) ?
The integral from 0 to 1 of x^3sqrt(7+5x^4) is (24sqrt(3)-7sqrt(7))/(30)