What is the integral from 0 to 2 of (3x-1)^{54} ?

The integral from 0 to 2 of (3x-1)^{54} is (5^{55}+1)/(165)

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integral from 0 to 2 of (3x-1)^{54}

\int_{0}^{2} (3 x - 1)^{54} d x

\frac{5 ^{55} + 1}{165}

Solution steps

\int_{0}^{2} (3 x - 1)^{54} d x

Apply u-substitution

: \int_{- 1}^{5} \frac{u ^{54}}{3} d u

= \int_{- 1}^{5} \frac{u ^{54}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{- 1}^{5} u^{54} d u

Apply the Power Rule

: [\frac{u ^{55}}{55}]_{- 1}^{5}

= \frac{1}{3} [\frac{u ^{55}}{55}]_{- 1}^{5}

Compute the boundaries:

\frac{5 ^{54}}{11} + \frac{1}{55}

= \frac{1}{3} (\frac{5 ^{54}}{11} + \frac{1}{55})

Simplify

= \frac{5 ^{55} + 1}{165}

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What is the integral from 0 to 2 of (3x-1)^{54} ?
The integral from 0 to 2 of (3x-1)^{54} is (5^{55}+1)/(165)