What is the integral from 1 to 3 of 3x(x^2-5)^5 ?

The integral from 1 to 3 of 3x(x^2-5)^5 is 0

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integral from 1 to 3 of 3x(x^2-5)^5

\int_{1}^{3} 3 x (x^{2} - 5)^{5} d x

0

Solution steps

\int_{1}^{3} 3 x (x^{2} - 5)^{5} d x

Take the constant out:

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

= 3 \cdot \int_{1}^{3} x (x^{2} - 5)^{5} d x

Apply u-substitution

: \int_{- 4}^{4} \frac{u ^{5}}{2} d u

= 3 \cdot \int_{- 4}^{4} \frac{u ^{5}}{2} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int_{- 4}^{4} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{- 4}^{4}

= 3 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{- 4}^{4}

Simplify

3 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{- 4}^{4} : \frac{3}{2} [\frac{u ^{6}}{6}]_{- 4}^{4}

= \frac{3}{2} [\frac{u ^{6}}{6}]_{- 4}^{4}

Compute the boundaries:

0

= \frac{3}{2} \cdot 0

Simplify

= 0

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What is the integral from 1 to 3 of 3x(x^2-5)^5 ?
The integral from 1 to 3 of 3x(x^2-5)^5 is 0